Doctoral Dissertation
博士論文
Laser Excitation of Confined
Positronium in Porous Materials for
Rapid Cooling（高速冷却を目指した多孔質材料中におけるポジトロニウムのレーザー励起）

A Dissertation Submitted for the Degree of Doctor of Philosophy
December 2019
令和元年 12 月博士（理学） 申請

Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科
物理学専攻
Kenji Shu
周 健治

Abstract
Rapid cooling of positronium (Ps) is an essential technique to improve precision of testing
fundamental theories, and to realize the first Bose-Einstein condensation with antimatters. It
was recently proposed that Doppler laser cooling of Ps confined in a porous material is eﬃcientenough to achieve such targets. In this process Ps is excited many times inside nano pores. It
was, however, reported that decay of the excited Ps into annihilation γ-rays was enhanced innano pores and a line width of the resonace was broadened, both of which make the proposedcooling method useless. In that report, the decay of Ps in the ground state was also enhanced
by being possibly trapped at some contaminants remaining on the surface of the pores, and theorigin of the abnormal phenomena was attributed to the formation of such surface state. In thisthesis, a Ps confining cavity which did not have the contaminants aﬀecting Ps in the ground state
was fabricated, and laser excitations of Ps in the pores were performed. The excited Ps had thesimilar enhancement of the decay and broad resonance spectrum also in the new cavity to favorthat some of the distinctive features of the excited state, such as the small binding energy orhigh electric susceptibility, are origins of the abnormal phenomena. In order to quantitativaly
estimate the decay rate and the broadening eﬀect of the excited Ps, a realistic model was newly
constructed with including those parameters. It was measured for the first time that the decayrate was in the order of 1 THz and depended on kinetic energy of Ps. The width of the resonancespectrum was broadened as wide as 1 nm in FWHM but independent on the decay rate. Thisfavors that the broadening is induced by other machanisms from the enhanced decay. Possible
mechanisms of both of the enhanced decay and the broadening , and future works to elucidatethem are discussed following the measurements.

iContents
1 Introduction
1.1 Properties of positronium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Internal states and decay modes . . . . . . . . . . . . . . . . . . . . .
1.1.2 Interactions with material . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Cooling of Ps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 New method of rapid cooling . . . . . . . . . . . . . . . . . . . . . . .
1.3 Enhanced decay and broadening eﬀect of confined 2P-Ps . . . . . . . . . . . .
1.3.1 Observations with porous silica material which aﬀected 1S-Ps . . . . .
1.3.2 Aims of the present work . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
2
3
6
6
7
8
8
8

2 Experimental Setup
2.1 Positron supplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Accelerator based slow positron production . . . . . . . . . . . . . . .
2.1.2 Retarding bias to block slower positrons’ contamination . . . . . . . .
2.1.3 Magnetic focus lens . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Positronium converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Silica aerogel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Measurement of Ps lifetime in the aerogel . . . . . . . . . . . . . . . .
2.2.3 Capping by non-porous silica film . . . . . . . . . . . . . . . . . . . .
2.2.4 Ps confinement by the capping . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Mount on sample holder . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Optical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Hardware and specification . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Path of lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Gamma-ray detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11
11
13
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14
16
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17
17
19
19
21
24
24
26
27
32
32

3 Analysis Methods
3.1 Method based on an averaged waveform (SSPALS) . . . . . . . . . . . . . . .
3.2 Pulse-by-pulse analysis method . . . . . . . . . . . . . . . . . . . . . . . . . .

35
35
38

iii

3.3

Quality check of analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Decay rate and production probability . . . . . . . . . . . . . . . . . .
3.3.2 Energy of gamma-rays from Ps decay . . . . . . . . . . . . . . . . . .
Model of excitation and decay of 2P-Ps . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Equations of internal states . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Predictions by the model . . . . . . . . . . . . . . . . . . . . . . . . .

38
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46
48
48
49

4 Results and discussion
4.1 Demonstration of Ps Lyman-α transition in vacuum . . . . . . . . . . . . . . .
4.2 Observation of the enhanced decay and the broadening for confined 2P-Ps . . .
4.2.1 Decay mode of the confined 2P-Ps . . . . . . . . . . . . . . . . . . . .
4.2.2 Adaptability of the decay model . . . . . . . . . . . . . . . . . . . . .
4.3 Quantitative analysis of the broadening and the decay rate . . . . . . . . . . . .
4.3.1 Estimations of the width of the broadening and the decay rate . . . . .
4.3.2 Dependence of the enhanced decay on radicals induced by the UV laser
4.3.3 Less pick-oﬀ decay by the energy selective decay of 2P-Ps . . . . . . .
4.3.4 Consistency between the analysis methods . . . . . . . . . . . . . . . .
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Broadening eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Decay process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.3 Outlook for the rapid cooling of Ps . . . . . . . . . . . . . . . . . . . .

53
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58
60
60
65
66
66
69
69
71
72

5 Conclusion

73

Acknowledgements

75

3.4

iv

List of Figures
1.1
1.2
1.3
1.4
1.5
1.6

Properties of Ps in various internal states . . . . . . . . . . . . . . . . . . . . .
Schematic description of the RTE model . . . . . . . . . . . . . . . . . . . . .
Lifetimes and pick-oﬀ decay rates calculated for various conditions by RTE model
Dependences of the pick-oﬀ decay rate on temperature of Ps . . . . . . . . . .
Time evolution of temperature of Ps in silica aerogel . . . . . . . . . . . . . .
Simulated time evolutions of temperature of Ps with the new cooling method .

2.1 Picture of the experimental setup . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Drawings of the experimental chamber to excite Ps confined in the Ps converter
2.3 Timing profile of the positron pulse . . . . . . . . . . . . . . . . . . . . . . .
2.4 Spacial profile of the positron beam . . . . . . . . . . . . . . . . . . . . . . .
2.5 Drawing including the blocker of the slower positrons. . . . . . . . . . . . . .
2.6 Configuration and magnetic field of positron focusing . . . . . . . . . . . . . .
2.7 Timing spectrum of annihilation γ-rays from Ps in the aerogel using Na-22 . . .
2.8 Schematic view of a geometrical configuration to confirm the confinement of Ps
2.9 Recovered lifetime of o-Ps by confinement . . . . . . . . . . . . . . . . . . . .
2.10 Magnified drawing around the sample holder . . . . . . . . . . . . . . . . . .
2.11 Optical transmittance of silica aerogel . . . . . . . . . . . . . . . . . . . . . .
2.12 Picture of the aerogel showing fluorescence by UV laser irradiation . . . . . . .
2.13 Fluorescence spectra of aerogel excited by UV lights . . . . . . . . . . . . . .
2.14 Intensities of fluorescent peaks versus excitation wavelength . . . . . . . . . .
2.15 Time profile of the UV laser . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 Transmittance spectrum through solid etalon for line width measurement . . . .
2.17 Timing jitter of the OPO laser . . . . . . . . . . . . . . . . . . . . . . . . . .
2.18 Photoionization probability by lasers . . . . . . . . . . . . . . . . . . . . . . .
2.19 Drawings of the setup to excite Ps in vacuum . . . . . . . . . . . . . . . . . .
2.20 Multiple reflector for eﬃcient excitation of Ps travelling in vacuum . . . . . . .
2.21 Path of the lasers to excite Ps in vacuum . . . . . . . . . . . . . . . . . . . . .
2.22 Response waveform of the γ-ray detector . . . . . . . . . . . . . . . . . . . . .
2.23 Energy resolution of the γ-ray detector . . . . . . . . . . . . . . . . . . . . . .
2.24 Timing resolution of the γ-ray detector . . . . . . . . . . . . . . . . . . . . . .
2.25 Input geometry in the Geant4 Monte Carlo simulation . . . . . . . . . . . . . .
2.26 Energy spectra by Monte Carlo simulation. . . . . . . . . . . . . . . . . . . .
v

2
3
4
5
6
7
12
12
13
14
15
16
18
19
20
20
21
22
22
23
24
25
26
27
28
28
29
30
31
31
32
33

3.1 Typical waveforms of the output of the PMT in the full range . . . . . . . . . .
3.2 Typical waveforms of the output of the PMT in the enlarged range . . . . . . .
3.3 Characteristic function of the high-pass filter . . . . . . . . . . . . . . . . . . .
3.4 Comparison of raw and filtered waveforms . . . . . . . . . . . . . . . . . . . .
3.5 Height spectra of the filtered pulses’ peaks . . . . . . . . . . . . . . . . . . . .
3.6 Energy resolution of filtered waveform analysis . . . . . . . . . . . . . . . . .
3.7 Timing spectra of the filtered pulses’ peaks . . . . . . . . . . . . . . . . . . .
3.8 Timing profile of the positron beam during data acquisition . . . . . . . . . . .
3.9 SSPALS analysis on the capped aerogel data . . . . . . . . . . . . . . . . . . .
3.10 Pick-oﬀ decay rates in the capped aerogel by the SSPALS analysis . . . . . . .
3.11 SSPALS analysis on the uncapped aerogel data . . . . . . . . . . . . . . . . .
3.12 Pick-oﬀ decay rates in the uncapped aerogel by the SSPALS analysis. . . . . . .
3.13 Filtered waveforms and detected peaks in the pulse-by-pulse analysis . . . . . .
3.14 Timing spectra of o-Ps decays through the pulse-by-pulse analysis . . . . . . .
3.15 Comparison of timing spectra with and without the high-pass filter . . . . . . .
3.16 Energy spectrum of annihilation γ-rays from o-Ps by the pulse-by-pulse analysis.
3.17 Simulated laser field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.18 Example of density matrix by the model calculation of the Ps excitation . . . .
3.19 Example of ΓL by the model calculation of the Ps excitation . . . . . . . . . . .
3.20 Calculated resonance spectra of the enhanced decay of 2P-Ps . . . . . . . . . .

36
37
39
40
40
41
41
43
43
43
44
44
45
46
47
47
50
50
51
51

4.1 Timing and energy spectra of annihilation γ-rays from Ps excited in vacuum . .
4.2 Timing spectrum by irradiating only UV laser on Ps in vacuum . . . . . . . . .
4.3 Resonance spectrum of Ps Lyman-α transition in vacuum . . . . . . . . . . . .
4.4 PMT waveforms with and without the UV laser. . . . . . . . . . . . . . . . . .
4.5 Timing spectra of the γ-rays increased by the UV laser . . . . . . . . . . . . .
4.6 Resonance curve of I L in wide range of wavelength . . . . . . . . . . . . . . .
4.7 Energy spectrum of γ-rays increased by the UV laser . . . . . . . . . . . . . .
4.8 SSPALS analysis on the waveform with the laser . . . . . . . . . . . . . . . . .
4.9 Resonance spectra and timing scan of I L . . . . . . . . . . . . . . . . . . . . .
4.10 Uncertainty of time evolution of Ps kinetic energy . . . . . . . . . . . . . . . .
4.11 Magnified views of the uncertainty of time evolution of Ps kinetic energy . . .
4.12 Energy dependence of the decay rate of 2P-Ps . . . . . . . . . . . . . . . . . .
4.13 Energy dependence of the decay probability of 2P-Ps per a collision . . . . . .
4.14 Timing spectra measured at diﬀerent accumulations of the radicals . . . . . . .
4.15 Decreases of the pick-oﬀ decay rates by energy selective 2P-Ps decay . . . . . .
4.16 Decrease of kinetic energy by energy selective 2P-Ps decay . . . . . . . . . . .
4.17 Comparisons of measured integrated decay rate between analysis methods . . .
4.18 Calculated shifts of the binding energy of Ps under electric field . . . . . . . .
4.19 Schematic drawing of silica nano particles . . . . . . . . . . . . . . . . . . . .
4.20 Calculated shifts of the self decay rate of o-Ps under electric field . . . . . . . .

54
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55
56
56
57
58
59
61
63
63
64
65
66
67
67
68
70
70
71

vi

List of Tables
2.1
2.2
2.3
2.4
2.5
2.6
2.7

Properties of the positron beam . . . . . . . . . . . . . . . . . . . . . . . . . .
Properties of the silica aerogels . . . . . . . . . . . . . . . . . . . . . . . . . .
CVD parameters of non-porous silica capping . . . . . . . . . . . . . . . . . .
Specification of the UV laser . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specification of the solid Fabry-Pérot etalon to measure UV laser line width . .
Parameters to reproduce the response waveform of the γ-ray detector . . . . . .
Simulated detection eﬃciencies and mean deposition energies . . . . . . . . .

13
17
18
24
25
30
33

4.1
4.2

Uncertainties of estimation of I L from measurements and analysis . . . . . . .
Uncertainties of estimation of I L from the decay model of Ps . . . . . . . . . .

62
62

vii

Chapter 1

Introduction
Positronium (Ps), which is a bound state of an electron and a positron, is an excellent system
to study fundamental physics. One of the breakthroughs for the study is to develop an eﬃcientmethod of cooling Ps down to several Kelvins. I and the collaborators proposed a new method
which combined thermalization processes and Doppler laser cooling for Ps confined in a porous
material [1]. Excitations of Ps into the 2P state in the pores must be repeated many times in themethod, but a recent experiment reported that the cycle would be impossible because confined Ps
in nano pores of silica (SiO2 ) rapidly decayed into annihilation γ-rays by the excitation, and thewidth of the resonance spectrum was abnormally broadened [2]. Mechanisms of this enhanced
decay and the broadening have been totally unknown while it was suggested that Ps formed a statestrongly aﬀected by the material and this state had the large decay rate when excited into the 2P
state. The formation of the state was assumed by disagreements between measured lifetimes ofconfined Ps in the 1S ground state (1S-Ps) and conventional models. It is necessary to elucidate
the mechanisms of the enhanced decay and the broadening to develop a new Ps confining cavity
which is able to be used for the method of cooling. The present work aims to test the proposed
assumption by exciting Ps into the 2P state (2P-Ps) confined in a silica aerogel, in which the
decay rate of 1S-Ps agreed with the conventional model, and to quantitatively measure the decayrate and the width of the resonance of 2P-Ps to provide clues for identifying physical processesof the abnormal phenomena.

1.1 Properties of positronium
Positronium (Ps) is a bound state of an electron and a positron. It has been an excellent system
for studying fundamental physics thanks to its simple and exotic composition. Ps consists of
only leptons so that precise tests of Quantum Electrodynamics (QED) have been performed [3]through calculations and measurements of decay rates [4–7] and various energy intervals ofinternal states [8–10]. The exotic feature that Ps consists of the pair of the matter and antimatterhas allowed to search for CP violation in the lepton sector [11] and exotic decays mediated by
new physics beyond the Standard Model [12–14].
1

Energy (eV, not in scale)

1 𝜇s
3𝛾 decay3 ms
3𝛾 decay

−1.7

1 ns
2𝛾 decay

𝐿=1

𝐿 = 1 (P-state)> 100 𝜇s for any fine structures
2𝛾 decay

𝐿=0

Lyman-𝛼Δ𝐸 = 5.1 eV
𝜆 = 243 nm
𝜏 = 3.2 ns

𝑛=2
𝑛=1

−6.8

𝐿 = 0 (S-state)

125 ps2𝛾 decay

142 ns3𝛾 decay

𝑇𝑜𝑡𝑎𝑙 𝑠𝑝𝑖𝑛 0
p-Ps

𝑇𝑜𝑡𝑎𝑙 𝑠𝑝𝑖𝑛 1
o-Ps

Figure 1.1: Properties of Ps in various internal states. Decay modes, lifetimes, and details of
the Lyman-α transition are noted. L represents the azimuthal quantum number for the orbital
angular momentum.

1.1.1 Internal states and decay modes

Ps has various decay rates and modes into annihilation γ-rays depending on its internal structures.
Main decay modes are 2γ decay into mono energetic 511 keV γ-rays in back-to-back directions,and 3γ decay in which γ-rays with continuous energy spectra are resulted. Decay modes are
determined by C and P symmetry, and the decay rates depend on scattering amplitudes to eachmode and overlaps of the eigen wave functions of the positron and the electron. Figure 1.1
summarizes the decay modes and lifetimes for the principal quantum number n = 1 and 2 [15–18]. Features of o-Ps in the 1S (n = 1, L = 0) and the 2P (n = 2, L = 1) states are important forthe present work. Ps represents o-Ps hereafter if not specified. Observations of the long lifetimeand the continuous energy spectrum of annihilation γ-rays can be evidences of productionsof o-Ps in the 1S state. 2P-Ps have very long lifetimes for self annihilations, but the short
lifetime (3.2 ns) of the spontaneous decay into the 1S state. The Lyman-α transition of Ps canbe induced by 243 nm UV light, and is the best transition for laser cooling because of the short
lifetime and availability of a laser system at the wavelength.
2

|𝜓#$ |%

𝛿 ≃ 0.18 − 0.19 nm|𝜓#$ |%∝ pore sizeState with low center of motion energy→ Small overlap, less pick-off decay

State with high center of motion energy→ Large overlap, more pick-off decay

Figure 1.2: Schematic description of the RTE model. Pore surfaces are modeled as infinite
potential barriers. Overlaps between the probability amplitude and the thin skin region from thesurfaces (δ ≃ 0.18 nm) determine the pick-oﬀ decay rate.

1.1.2 Interactions with material
Ps can be produced by irradiating a positron to suitable materials. Silica (SiO2 ) is one of thematerials with high Ps production probability [19]. Materials also aﬀect produced Ps throughvarious interactions to result in variations of the lifetime and kinetic energy. Information of Ps
can be obtained by measuring those eﬀects. Major interactions related to the present work are
introduced hereafter.
Pick-oﬀ decay
The lifetime of 1S-Ps in materials depends on sizes of internal pores or voids if exist because
the pair annihilations occur between the positron in Ps and an electron in the material. This
decay process is called pick-oﬀ decay [20, 21], and dependences of the pick-oﬀ decay rate onpore size and kinetic energy of Ps can be predicted by so-called Rectangular Tao-Eldrup (RTE)model [22, 23]. Figure 1.2 shows a schematic description of the model. In the RTE model,
pore surfaces are modeled as infinite potential barrier, and the distances between barriers are
determined so that a mean free path in pores of the material is reproduced. The RTE model
assumes a rectangular shape for the space surrounded by the barriers. The pick-oﬀ decay rate canbe calculated by assuming that Ps has a spin-averaged decay rate (0.25/125 ps + 0.75/142 ns)
if it exists within the distance of δ ≃ 0.18 nm from the barriers. The model can be considered
to be valid for materials which have a negative work function for Ps, such as silica with around−1 eV because the negative work function validates the picture that Ps behaves like free particle
in the square well potential without strongly aﬀected by the material. An agreement between ameasured lifetime of 1S-Ps and the prediction by the RTE model is a good signature that 1S-Ps
3Pick-off decay rate (µs-1)

Lifetime (ns)

140
120
100
80

0K

60

298 K

40

600 K

20

900 K

0
1

10

102
Mean free path (nm)

103
102
10
1
−1

10

10−2
0

(a) In lifetimes.

20

40

60
80
100
Mean free path (nm)(b) In decay rates.

Figure 1.3: Dependence of the pick-oﬀ decay rate on mean free path for various temperatures ofPs.

is not bounded to the surface.
In the previous work [2], the possible formations of the state which were bounded to thesurface of the pores were assumed from shorter lifetimes of 1S-Ps than the predictions of the
RTE model.
Formations of the surface state, which is the suspected origin of the abnormal behaviors of
2P-Ps, would be verified through measurements of the pick-oﬀ decay rate in the present work.
The pick-oﬀ decay rate depends on kinetic energy of Ps and pore sizes because the overlapping ratio between Ps wave function and the thin skin (δ) from the surfaces depends on thoseparameters. δ was empirically determined to reproduce measured lifetimes of o-Ps in pores
whose sizes were able to be assumed by other methods. Figure 1.3 show dependence of lifetimes and the corresponding pick-oﬀ decay rates on mean free path for various temperatures of
Ps. The pick-oﬀ decay will also occur even for stopped Ps with 0 K because it is impossible
for particle to be fully localized away from the surface in the quantum mechanics. This quantum eﬀect is significant√ especially for Ps, whose small mass leads to a large de Broglie wavedB
length (λPs = 0.87 nm 1 eV/EPs ). The pick-oﬀ decay rate can be approximated by a linear function on kinetic energy or temperature of Ps if the quantum eﬀect is small [22]. Figure 1.4 show
dependences of the pick-oﬀ decay rate on temperature of Ps with and without the approximation
for a mean free path of 40 nm. Both results agree in 10 % accuracy at more than 50 K for themean free path.
Spin exchange interactions
Spin exchange interactions, in which the spin of a consisting particle in o-Ps is flipped to form pPs, also decrease the eﬀective lifetime of o-Ps because p-Ps has much less lifetime [24–26]. Thisquenching interactions can be occurred between paramagnetic radicals which can be induced byirradiation of UV light on the material. It was demonstrated for silica based materials that the
productions of the radicals could be suppressed by proper treatments of chemical groups on thesurface of the material [24].
4Pick-off decay rat

0.2

4

1000

1500

2
1
0

2000
T (K)

With approximation
Without
approximation
µT

0

500

1000

1500

2000
T (K)

0

500

1000

1500

2000
T (K)

1

3
0.8

2
1
0

2000
T (K)

500

Ratio

Pick-off decay rate (µs-1)

0

3

0.6

0

500

1000

1500

2000
T (K)

Ratio

1500

0.4

Figure 1.4: (Left) Dependences of the pick-oﬀ decay rate on temperature of Ps with and without
1
the approximation.
(Right) Ratio of the results. Both results agree in 10 % accuracy at morethan 50 K.
0.8

0.6
Thermalization
0

500

1000

1500

2000
T (K)

Ps is thermalized to temperature of the surrounding material through energy exchanging processes. From an initial temperature around 10 000 K, which is determined from work functionsof the material for Ps, this thermalization process typically takes the same order of time as the
lifetime of o-Ps. Time evolution of kinetic energy of Ps, E, can be modeled by a classical elastic
collision model [27] as
)
(
2 √
3
dE
=−
2mPs E E − k B T ,
dt
LM
2

(1.1)

where L is a mean free path of collisions, M is a mass of bodies to be collided with, mPs is themass of Ps, k B is the Boltzmann constant, and T is a temperature of the surrounding material. It
was also suggested that an introduction of dependence of M on E would enable to describe thethermalization process in a wide range of E where inelastic scatterings or quantum size eﬀects
took eﬀect. I and collaborators measured time evolutions of temperature of Ps confined in a silica
aerogel, which is a highly porous material made by silica, at cryogenic temperatures [28, 29].
Figure 1.5 shows the results of the measurements. The process in which Ps lost its kinetic energy
was clearly observed. L was estimated as around 40 nm by the gas adsorption measurement.
Temperatures of Ps were evaluated by the pick-oﬀ decay rates (⟨Γpo ⟩) averaged in each timing
windows. The conversion from ⟨Γpo ⟩ to temperature of Ps was performed according to the RTE
model. The vertical axis shows the ratio of ⟨Γpo ⟩ over the self decay rate Γs of o-Ps. The time
evolutions were able to be reproduced by introducing the dependence of M on E. Time evolutionof kinetic energy of Ps is estimated according to these measurements in the present work.
5

295K
210K
130K
25K

0.1

500
400

T Ps (K)

Γ"# 〈Γ/2〉Γ/ &Γ3

0.15

300
200

0.05

100
0

0

0
400
600
Time (ns)200

Figure 1.5: Time evolution of temperature of Ps in the silica aerogel. Legends in the figure showtemperatures of the aerogel. The temperatures of Ps were evaluated by the pick-oﬀ decay rates
at each timing window.

1.2 Cooling of Ps
1.2.1 Motivations
Cold Ps will be beneficial to advance the study on fundamental physics, and also be usefulfor industrial applications. A current target is to develop a method to cool Ps down to several
Kelvins. This will enable to test CPT invariance and an existence of “antigravity”, and to realize
Bose–Einstein condensation of Ps.
Productions of cold Ps at less than 10 K will increase the precision of the spectroscopic
measurement of the 1S–2S energy interval of o-Ps by an order of magnitude [30, 31]. As
discussed in the work which measured the interval with the highest precision [9], the high Ps
temperature around 600 K in the work contributed most significantly to the systematic uncertainty.
The fast motion of Ps resulted in the large second order Doppler shift and short time duration
while Ps interacted with laser fields. The latter eﬀect required strong laser fields which inevitablycaused large AC Stark shift, and also led to large transient broadening. The medium velocity ofPs will be reduced by around factor 8 through the cooling. It was estimated that the systematic
uncertainty would be reduced by around an order of magnitude. With the improved precision, themass diﬀerence of a positron and an electron, which would arise if CPT invariance was broken,
will be measured in the highest precision by measuring the interval [9, 32]. The improvement
will be also large enough to test a tiny shift on the interval which would be caused by hypothetical
repulsive gravitational force between the earth and a positron if assumed that antimatters had thenegative gravitational mass whose absolute was same as the inertial mass. This “antigravity”
could possibly explain the accelerating expansion of the universe without introducing the darkenergy [33], while the ideas are still theoretically controversial [34, 35].
A realization of Bose–Einstein condensation (BEC) of Ps is another desirable application inwhich the cold Ps plays a critical role. Ps is one of the most promising systems to realize the first6

Temperature (K)Only by thermalization
With laser coolingTc with n0=4×10%& cm()
With laser cooling
Only by thermalization

Time (ns)Figure 1.6: Simulated time evolutions of temperature of Ps and the critical temperature Tc of
the BEC transition under the new scheme of the cooling. The BEC transition will be observedat around 300 ns later from the productions of Ps with the initial density of 4 × 1018 cm−3 .
The remained density with the laser was higher than that without the laser because of the longannihilation lifetime of the 2P states.
BEC with antimatters [36] because of the following two merits for achieving the high enoughphase space density necessary to cause the BEC transition:
1. High critical temperature as 14 K at 1018 cm−3 thanks to its light mass.
2. Availability of producing a denser cloud of Ps than any other systems with antimatters.
Cooling of Ps down to several Kelvins has been under intense study [1, 37] because recent
progresses of positron accumulation [38, 39] and focusing [40, 41] suggested that a dense Ps as1017 cm−3 –1018 cm−3 would be available in the near future. Ps-BEC will be an antimatter laser
which can be used for a Mach–Zehnder interferometer. The sensitivity of the interferometer will
be largely increased by the high coherence of the BEC state so that the gravity eﬀect on Ps will
be measured [42]. Another unique application by Ps-BEC is to generate 511 keV γ-ray laser [43,44]. High coherence of the γ-rays is expected thanks to collective decays from the BEC state.
The γ-ray laser can be used for such as non destructive inspections of infrastructures.

1.2.2 New method of rapid cooling
I proposed a new method of eﬃcient cooling [1] combining the thermalization process andDoppler laser cooling. Ps will be produced inside a porous silica material at cryogenic temperature, and be eﬃciently cooled down to around 200 K through the thermalization process. A
243 nm UV laser which induces the Lyman-α transitions will be irradiated on Ps in the material
for Doppler cooling. Figure 1.6 shows simulated time evolutions of temperature of Ps and thecritical temperature Tc of the BEC transition. A pore size was set to be 75 nm in the simulation.
7

The laser accelerate cooling from around 200 K and be eﬃcient enough to cool Ps down to lessthan 10 K in 350 ns from the productions of Ps. The BEC transition would be observed thanks
to both of the eﬃcient cooling and the extended annihilation lifetime of the 2P states if an initial
density as high as 4 × 1018 cm−3 was achieved. An essence of the method is to perform laser
cooling on confined Ps: this will bring two merits as (1) the two processes can eﬃciently cool
down Ps in the wide range of its kinetic energy, and (2) Ps can stay with a spot of the laser
irradiation by the confinement without which it escapes with large velocity.

1.3 Enhanced decay and broadening eﬀect of confined 2P-Ps
1.3.1 Observations with porous silica material which aﬀected 1S-Ps
The key process in the cooling method is to repeat the cycle of the Lyman-α transitions for Ps
confined in nano pores, but eﬀects on 2P-Ps by the material are not understood well. The firstexperimental demonstration of the Lyman-α transition of confined Ps was reported in 2011 [45].
For Ps confined in a porous silica material with around 5 nm pores, they observed a blue shift ofcenter and a narrowed width of the resonance spectrum. The shift was attributed to some eﬀects
from the material, and the narrowing to Dicke eﬀect [46], which suppresses Doppler broadening.
It was expected that large pores would ease those eﬀects, but another work in 2018 reported
that the width was conversely broadened and 2P-Ps immediately decayed into γ-rays in pores aslarge as 75 nm [2]. The broadened width was as wide as 2 nm in the wavelength (10 THz in thefrequency), which was too wide to be attributed to any known phenomena including Doppler
or the collisional broadening. Both of the eﬀects make the proposed cooling method uselessbecause the wide width inhibits Doppler shift which is used in laser cooling to selectively excite
the counter propagating Ps against to the laser, and the enhanced decay largely decreases theremained number of Ps after the cycles of the Lyman-α transitions.
Mechanisms of the broadening eﬀect and the enhanced decay must be elucidated, but only
limited information is available. One of the important observations in the previous work was thatmeasured lifetimes in the porous silica materials were shorter than the predictions by the RTE
model. The lifetimes were almost independent on pore sizes ranging from 5 to 75 nm for theirfour samples. They suggested that the short lifetimes originated from formations of bound states
between Ps and the surfaces of the pores. The formations of the surface state were assumed to
be induced by some contaminants remaining at isolated pores because the two eﬀects were notobserved in 2011’s work, which used a porous silica whose pores connected each other.

1.3.2 Aims of the present work
Following the observations, the present work has two main aims. The first one is to test theassumption that the surface state induced the broadening eﬀect and the enhanced decay by using
another type of porous silica material in which Ps is not bounded to the surface states in the 1S
state. Silica aerogels are used since lifetimes of 1S-Ps in those pores agree with the predictions
by the RTE model. This agreement favors that Ps moves almost freely in pores rather thanbeing bound to the surfaces. In the present work, Ps is produced in well characterized aerogels
and excited into the 2P state to investigate whether the broadening and the enhanced decay are8observed even without being bounded to the surface in the 1S state. The decay rate of 2P-Ps
is also quantitatively estimated by applying a realistic model which includes the decay rate tomeasured intensities of annihilation γ-rays. A dependence of the decay rate on kinetic energy of
Ps is also measured by changing timings of the laser irradiation. This is possible because kinetic
energy of Ps varies time by time through the thermalization process. The measured decay rate
will be useful information to identify physical processes to induce the abnormal behaviors of
2P-Ps.

9Chapter 2

Experimental Setup
Experiments were conducted at Slow Positron Facility (SPF) in High Energy Accelerator Research Organization (KEK) [47]. A dedicated setup at the B1 beam line of KEK-SPF was build
to measure the decay rate of 2P-Ps which were confined in a silica aerogel. The setup mainly
consisted of four parts:
1. Positron supplier. KEK-SPF supplied bunched positrons in a short pulse.
2. Positronium converter. It supplied electrons to the irradiated positrons to form Ps. Ps
might be trapped in pore networks of the converter.
3. Laser system. Pulse lasers were synchronized with the positrons to be irradiated on the
produced Ps. The lasers were used to excite Ps to the 2P state, and then possibly ionizing
2P-Ps into a dissociated positron and an electron.
4. γ-ray detector. Annihilation γ-rays were detected to measure the decay rates of Ps.
Figure 2.1 shows a picture of the setup. Figure 2.2 show drawings of a vacuum chamber toperform laser excitations of Ps confined in the Ps converter. Pressure in the vacuum was kept
less than 5 × 10−6 Pa. Each part is introduced in the following sections.

2.1 Positron supplier
Bunched positrons in short pulses can be supplied at KEK-SPF. Its shortness of the pulse duration
is an essential requirement to be synchronized with the pulse laser system. Table 2.1 summarizes
beam properties used in the experiments. The methods to evaluate the parameters are introducedin the following paragraphs. A brief review of KEK-SPF, and modifications applied on thepositron beam are introduced in the following subsections.
Intensity The intensity of the positrons at the Ps converter was estimated by that of annihilation
γ-rays measured by the detector, which is described in detail in section 2.4.
11

Upstream
Gamma-ray detector

Positrons

Laser
Feedthrough for
Ps converter
8

7

6

5

Downstream
4

3

2

1

Figure 2.1: Picture of the experimental setup.
F

Gamma-ray detector(LaBr3(Ce) scintillator)

E

Positronfocusing coil

PMT

MCP

Upstream
D

Laser

e+

Downstream
Samplemounted holder

Cold fingerC

Ps converter

10 cm

10 cm

B

Figure 2.2: Drawings of the experimental chamber to excite Ps confined in the Ps converter.
(Left) Cross sectional drawing of the chamber. (Right) Drawing inside the chamber from thedownstream of the beam line.
A

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Table 2.1: Properties of the positron beam. The intensity was estimated by that of annihilation
γ-rays. The timing and spacial profile were evaluated by the MCP.

Signal amplitude (V)Energy5 keVIntensity at Ps converter1 × 105 s−1

Pulse time duration

11 ns FWHM

Beam size

2.6 mm FWHM

Repetition

50 Hz

0.6

0.4

0.2

0
−20

0

20
Time (ns)Figure 2.3: Timing profile of the positron pulse measured by the MCP. Waveforms were averaged
over one minute data acquisition.
Timing profile The timing profile of the positron pulse was measured by a Micro-Channel
Plate (MCP, HAMAMATSU, F2222-21P). Figure 2.3 shows an averaged profile in one minute.
FWHM of the pulse was measured to be 11 ns. The signal was amplified by a fast preamplifier (ORTEC, VT120C).
Spacial profile The spacial profile was measured by imaging the phosphor screen of the MCP
at a position of the Ps converter. Figure 2.4 shows the spacial profile imaged by a CCD camera.
The beam size was estimated as 2.6 mm FWHM by fitting the profile by a 2D-Gaussian function.
The positron beam was focused by a magnetic lens, which is described in subsection 2.1.3.

2.1.1 Accelerator based slow positron production
KEK-SPF produces slow positron beams using a linear accelerator (LINAC) [47]. Positrons are
generated by pair creation processes from bremsstrahlung γ-rays. The γ-rays are emitted byshooting electrons which are accelerated by the LINAC into a tantalum converter. The positrons
are re-moderated by tungsten meshes to have kinetic energy of around 3 eV, which is determined
13

Brightness (arb.)

Y Position (mm)X Position (mm)Figure 2.4: Spacial profile of the positron beam. The image was averaged over one minute dataacquisition.
by a work function of tungsten for positrons. This converter/moderator system was biased to
5 kV so that the 5 keV positron beam could be obtained at experimental spaces in the ground
potential. The positron beam was guided to the experimental chamber for around 10 m by anaxial magnetic field generated by solenoid coils.

2.1.2 Retarding bias to block slower positrons’ contamination
Retarding high voltage bias was applied to block slower positrons which would arrive at thechamber later than the main pulse of the beam. In order to reflect the slower positrons tothe upstream, a blocker with three plates were introduced before the experimental chamber.
Figure 2.20 shows a drawing including the blocker assembly. The blocker assembly was placedaround 80 cm ahead from the position of the Ps converter. The three plates in the assembly had
a 30 mm aperture. Each aperture was covered by a tungsten mesh (30 µm for wires’ diameter,
93 % opening) to uniformly apply electric field. The plates were placed in parallel to each other,and the center plate was biased to 3.5 kV. The others were in the ground potential. Positrons
with lower energy than 3.5 keV are reflected to the upstream, but those with higher energy passthrough the assembly with retaining the original energy. The bias voltage was determined toachieve the best signal-to-noise ratio.

2.1.3 Magnetic focus lens
The positron beam, whose diameter was initially around 20 mm, was focused on the Ps converter
to increase an overlap with the laser (6 mm FWHM size). A magnetic lens which consisted of
14

8

7

F

6

5

4

3

2

1

F

To upstream
The blocker assemblyE

E

Biased plate
D

D

C

C

B

B

Solenoid coils
A

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Figure2.5: Drawing
including6 the blocker ofthe slower positrons.
The3 plate at the centerof theblocker assembly was biased in high voltage.

15

1

A2

Lens coil surroundedby the pole piece

Solenoid coils
beam pipe
Beam axis
200 G

Magnetic field on beam axis

100 G

0G

1m

Figure 2.6: Configuration and magnetic field of positron focusing. The geometry is shown by
cross sectional view and had the rotational symmetry around the beam axis.

a solenoid coil and a pole piece was installed. It generated concentrated magnetic field which
focused positrons by Lorentz force. Figure 2.6 shows a coil configuration including the lens andthe guiding solenoid coils, and calculated magnetic field on the beam axis by inputting currents
actually flowed. The currents were optimized to achieve the highest intensity in the spot sizeof the laser. The resulted beam had the reasonable size assumed by the initial beam size, energy
spreading of the beam, and a performance of the lens.

2.2 Positronium converter
Silica aerogels were used as the positron-to-positronium converter and Ps confining cavity in thepresent work. Aerogels have open pore networks with high porosities where Ps can be emittedwith high probability. A non-porous silica thin film was deposited to cap the pore network toprevent Ps from escaping into the outer vacuum. Decay rates of o-Ps inside the pores were
measured to be consistent with the RTE model. This agreement indicates that 1S-Ps is notbounded to the surface and moves almost freely in the pores of the aerogel. It is then possible
to test the assumption of the previous work [2] that the strong material eﬀect by which 1S-Ps isbounded on the surface is the origin of the enhanced decay of 2P-Ps and the broad resonancespectrum. The following sections describe production processes and examined properties of thesilica aerogel cavities.

2.2.1 Silica aerogel
Silica aerogels used in the experiments were supplied by Japan Fine Ceramics Center. Propertiesof the aerogels are summarized in Table 2.2. The thin shape was fabricated in custom for thepresent work to suppress a energy loss of the laser which was irradiated on Ps after transmitting
the aerogel.
16

Table 2.2: Properties of the silica aerogel used in the experiments. The mean free path was
calculated by the pore diameters assuming sphere shapes for pores.
Product name

SP-30

Surface chemical groups

SiOCH3 (hydrophobic)

Density0.12 g cm−3

Pore diameters

40 nm–50 nm

Mean free path

30 nm–37.5 nm

Porosity

95%

Thickness

0.5 mm

2.2.2 Measurement of Ps lifetime in the aerogel
The decay rate of 1S-Ps confined inside the pore network of the aerogel was measured to checkthe consistency with the RTE model. A Na-22 radioisotope was used as a positron source for thismeasurement. Figure 2.7 shows an acquired timing spectrum. Two silica aerogels with 1 mm
thickness sandwiched the source in this measurement. The origin of the timing was determinedby detecting 1275 keV γ-ray from Na-22 which is followed by the beta decay. A backgroundby accidental hits was subtracted. A decay rate of thermalized Ps was measured by fitting a
exponential function to the timing spectrum from 180 ns. The fitted curve is superimposed in
Figure 2.7. The acquired life time was 131 ± 2 ns (0.6 ± 0.1 µs−1 in the pick-oﬀ decay rate) andagreed with the prediction for the mean free path of 30 nm–37.5 nm by the RTE model as shownin Figure 1.3. This agreement favored that the assumed picture of the RTE model was valid
in the aerogels and 1S-Ps did not form the surface state through strong eﬀects by the material.
An intensity of the o-Ps component was 13 % in the spectrum. A production probability of Ps
was estimated as around 35 % by including mean stopping probability in the aerogels, detection
eﬃciency for 2γ decay from the prompt components and 3γ from o-Ps, and spin statistics forp-Ps and o-Ps. This eﬃcient production was reasonable for aerogels with high porosity.

2.2.3 Capping by non-porous silica film
The top surface of the aerogel from which the positrons were irradiated was capped by a thin
non-porous silica film to prevent Ps from escaping. The thickness of the film was confirmed to
be 75 nm by ellipsometry measurements of silicon wafers which were capped beside the aerogel.
Around 70 % of the positrons with 5 keV energy was expected to penetrate the film to reach thepore network of the aerogel. The capping was conducted by the plasma enhanced chemical vapor
deposition (PE-CVD) process. Tetraethyl orthosilicate (Si(OC2 H5 )4 , TEOS) and oxygen (O2 )gasses were mixed to be used as base materials for the SiO2 film. Capping parameters are listed
in Table 2.3
17Counts (/1.6ns)

107

χ2 / ndf106

0_const272 / 259

Prob

0.27692.906e+06 ± 2.128e+04
131.1 ± 1.8

1_life2_flatBG −0.0004975 ± 21.4031925

105
104
103
102

0

200

400

600
Time (ns)Figure 2.7: Timing spectrum of annihilation γ-rays from Ps in the aerogel using Na-22. The
measured lifetime agreed with the prediction from the RTE model. It implies that 1S-Ps is notbounded to the surface of the silica aerogel.

Table 2.3: Parameters of CVD process for non-porous silica capping
TEOS gas flow

10 sccm

O2 gas flow

400 sccm

Deposition time

110 s

Substrate temperature

120 ◦C

18

5 keVe+Ps

aerogelBaF2

Figure 2.8: Schematic view of a geometrical configuration to confirm the confinement of Ps.
The BaF2 detector had less detection eﬃciency for escaped Ps so the lifetime would become
spuriously short by the escape.

2.2.4 Ps confinement by the capping
The confinement of Ps by the cap was confirmed by lifetime measurements using a slow positron
beam at National Institute of Advanced Industrial Science and Technology (AIST). A geometryof the measurement was set up as shown in Figure 2.8 to be sensitive for the escape of Ps into theouter vacuum of the aerogel pores. Positrons at the beam line of AIST are supplied by LINAC
based pair productions, and then timing of their irradiation is controlled by a electric chopper. If
Ps produced in the aerogel escaped, a decay component with a spuriously short lifetime would
be obtained because the BaF2 detector had lower detection eﬃciency for escaped Ps. Figure 2.9
compares timing spectra of annihilation γ-rays obtained by aerogels with and without the cap.
The origin of the timing was determined by triggers of the chopper. The lifetime was spuriously
short without the cap by the escape, but the cap recovered the lifetime to the same value asmeasured in the bulk. The confinement of Ps was successfully demonstrated.

2.2.5 Mount on sample holder
Samples including the aerogels with and without the cap were mounted on the holder withsandwiched by the tungsten mesh and plates with a 10 mm aperture. Figure 2.10 shows amagnified drawing around a sample holder. The mesh was put to prevent possible charge up of
the samples by the positron irradiations. The samples were pressed by four spring coils whichwere attached to the plates to realize better contact with the mesh and the holder. The weightwas 400 gf per coil. A kapton film, which is a polyimide film fabricated by Du Pont company,
was also mounted for calibration measurements since simple analysis was possible due to lessformation of Ps inside it.
19With cap
t=126.6±1.7 ns
I = 24.5%
Without cap
t=84.5±1.5 ns 7
I = 19%

8

6

5

F

Figure 2.9: Timing spectra of annihilation γ-rays obtained by aerogels with and without thecap. With the cap, the lifetime was recovered to the same value as measured in the bulk byconfinement.
Magnified view around the sample
Sample10 mm

Copper platewith the aperture

E

8

7

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5

4

3

2

1

Spring coilF

F

Tungsten mesh
E

E

D

Laser
e+

D

D

C

C

CFigure 2.10: Magnified drawing around the sample holder. The samples were sandwiched andB

Bpressed by the tungsten mesh and copper plates with a 10 mm aperture.
20

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Transmittance (%)

100
Measured80

Rayleigh scattering

60
40
20
0
200

300

400

500

600 700 800
Wavelength (nm)Figure 2.11: Optical transmittance of silica aerogel. The dependence on wavelength down to
300 nm was able to be described well by Rayleigh scatterings. 85 % of 243 nm light transmitted
the sample.

2.2.6 Optical properties

Optical transmittance and absorption of the aerogel were studied because the laser was also
irradiated on the aerogel to excite confined Ps. Figure 2.11 shows an optical transmittance of
the aerogel measured by a spectrophotometer (JASCO, V-770). High enough transmittance as
85 % for 243 nm light, which is the Lyman-α wavelength of Ps, was achieved for the thin aerogel
adopted in the present work. Transmittance down to 300 nm was well described by dependenceof Rayleigh scatterings (exp(−λ−4 )) as superimposed in the figure.
Absorptions and following fluorescence were observed in UV region. Figure 2.12 showsa picture of the aerogel irradiated by laser with 243 nm wavelength.
Fluorescence by UV
laser irradiation was observed while 243 nm light is invisible for human eyes. Other materials
made by silica, such as a view port window or a wafer, also exhibited the similar fluorescence.
These could be originated from impurities in silica or multi-photon processes. Intensities of thefluorescence excited by UV lights were measured by a spectro fluorometer (JASCO, FP-8500).
Figure 2.13 shows intensities of fluorescence lights excited by UV light whose wavelength wasscanned from 233 to 253 nm. Four peaks were observed and the intensity of each peak wasmeasured by scanning the excitation wavelength. The results of the scan are shown in Figure 2.14.
Bandwidths of the excitation light were expected to be 2.5 nm, and wavelength accuracy 1 nm by
the device’s specification. No peak was observed at the wavelength of Ps Lyman-α (243 nm). If
the enhanced decay of Ps was observed, the presence of the resonance would be able to determine
whether the decay was induced by Ps Lyman-α transitions or some phenomena related with thelight absorptions.
21

UV irradiation spot

AerogelFigure 2.12: Picture of the aerogel showing blue fluorescence by UV laser irradiation.

Figure 2.13: Fluorescence spectra of aerogel excited by UV lights. Four peaks were observed.

22

Figure 2.14: Intensities of fluorescent peaks versus excitation wavelength. No peak was observedat the wavelength of Ps Lyman-α (243 nm).

23

Table 2.4: Measured specification of the OPO laser.

SIGNAL HEIGHT (V)Pulse energy

1 mJ

Pulse time duration

2 ns–5 ns

Line width (FWHM)

0.021 nm, 1.1 × 102 GHz

Beam diameter

6 mm

Repetition

10 Hz

0.15

0.1

0.05

0
−20

−10

0

10

20
TIME (ns)Figure 2.15: Time profile of the UV laser. The time duration of the laser pulse was assumed to
be in 2 ns–5 ns by including a rise time of a digitizer.

2.3 Laser system
2.3.1 Hardware and specification
A wavelength tunable laser (Continuum, Panther EX OPO) was used to induce the Lyman-αtransition of Ps. The OPO laser was pumped by a pulse Nd:YAG laser (Continuum, SureliteI-10). Specification of the OPO laser was measured and is summarized in Table 2.4. The output
wavelength was calibrated with accuracy of 0.03 nm by a wavemeter (Coherent, WaveMate
Deluxe). The pulse energy was measured by a thermal power meter (Ophir, 2A-BB-9).
A time profile of the pulse was measured by a fast photo detector (THORLABS, DET025A/M).
Figure 2.15 shows an output waveform by the detector. The time duration of the laser pulse wasassumed to be in 2 ns–5 ns by including a rise time of a digitizer (1.4 ns) described in section 2.5.
This was a reasonable duration for the adopted OPO laser.
The line width was estimated by a transmittance spectrum through a solid Fabry-Pérot etalon.
Table 2.5 summarizes specification of the custom-made etalon fabricated by SIGMAKOKI, andFigure 2.16 shows the transmittance spectrum. A spectrum profile of the laser was assumed to be
Gaussian, and a convolved spectrum with the transmittance of the etalon was fitted to the measured
24

Table 2.5: Specification of the solid Fabry-Pérot etalon to measure the line width of the UV laser.
Base material

Synthetic silica glass

Thickness

330 µmReflectance per surface

98 %

800
600
400
200
0
243.35

Amplitude (mV)

Amplitude sigma (V)

1000

250
200
150
100
50

243.4

0

243.45243.5
Wavelength (nm)Power (mW)

Transmitted power (arb.)

Measured points
Etalon’s sharp transmittanceLaser spectrum ⊛ Etalon transmittance

243.36243.38243.4243.42
243.44243.4
Wav

Figure 2.16: Transmittance spectrum through the solid etalon for line width measurement. The
450
5line width of the OPO laser was estimated to be 0.021 nm in FWHM.
400
350
300
250
200
150
c_1
100
25
50 c_20 c_3
243.36243.38243.4243.42
243.44243.46243.48243.5
c_4
Wavelength (nm)

4
3
2
1
0

243.36243.38243.4243.42
243.44
243.4
Wav

RawPulseTiming_ch0[0] {RawOverThresholdNhit_ch0 <= 1}

EntriesMean
Std Dev

5546
830
0.2607

Counts (arb.)

hTimingRawHit0

Counts (arb.)

wOverThresholdTiming_ch0[0] {RawOverThresholdNhit_ch0 <= 1}

hTimingRawPulseTiming

EntriesMean
Std Dev

70

5546
830.7
0.2969

6060
50

4040

670 ps FWHM

30

2020
10

829.5

830

830.5

831
Time (ns)

00

829.5

829.5

830

830.5

830.5

831

831.5
832
831.5
Time (ns)Time (ns)awPulseWidth_ch0[0] {RawOverThresholdNhit_ch0 <= 1}
hTimingRawPulseWidth

Entries Timing
5546
Figure 2.17:
diﬀerences between the trigger of the positron beam and the output of the
Mean
4.998
Std DevThe
0.2607
OPO laser.
jitter was 670 ps in FWHM.

5

5.5

6

points. The transmittance spectrum of the etalon was estimated by the specification. The line
width was estimated as 0.021 nm in FWHM. The corresponding bandwidth was 1.1 × 102 GHz.
The width was reasonable for the OPO laser, and narrow enough to measure the expectedresonance width of the transitions.
The OPO laser was synchronized with the positron beam. Timing of the irradiation was
tunable with less than 1 ns jitter by a delay generator (Stanford Research Systems, DG535).
Figure 2.17 shows a measured profile of timing diﬀerences between the trigger of the positron
6.5
7
7.5
FWHM anddurationthe(ns) output of the OPO laser.
beam
The jitter was much smaller compared with the time
duration of the pulse.
532 nm pulse lasers were also able to be irradiated to confirm the Lyman-α transition.
532 nm green lasers photoionize only 2P-Ps, which does not decay into annihilation γ-rays
without aﬀected by the material. 2P-Ps is dissociated into a positron and an electron, and thenthe annihilation of the positron becomes the signal of the transition. 1S-Ps is not photoionizedbecause energy of a 532 nm photon is lower than the binding energy of 6.8 eV. The Surelitelaser or another Nd:YAG laser (Spectra-Physics, GCR-250, 25 Hz repetition) were used as thephotoionization laser. Either laser was able to output 1 mJ–10 mJ pulses with the similar time
duration and beam size as the OPO laser. Figure 2.18 shows estimated photoionization rates andprobabilities per a pulse for both wavelengths [48]. 532 nm lasers were powerful enough while
photoionizations by 243 nm laser were negligible.

2.3.2 Path of lasers
The lasers were irradiated in two ways to perform types of the laser excitations. In one of which,the laser was irradiated on the aerogels in the counter propagating direction to the positron beam
as shown in Figure 2.2. The confined Ps in the aerogel was mainly excited by this configuration.
In the other way, the laser was irradiated at several millimeters away from the surface of the26

Ionization probability

Ionization rate (/ns)

1
10−1
10−2
10−3

532 nm

1

10−1

10−2

243 nm10−3

0 1 2 3 4 5 6 7 8 9 10
Pulse energy (mJ)

0 1 2 3 4 5 6 7 8 9 10
Pulse energy (mJ)

Figure 2.18: Photoionization rates and probabilities per a pulse by lasers. 532 nm lasers werepowerful enough and photoionizations by 243 nm laser were negligible.
uncapped aerogel by being reflected at mirrors put in the chamber. Figure 2.19 show drawingsof the modified chamber to allow the irradiation in this way. This configuration was adopted toexcite Ps emitted in the outer vacuum of the aerogel. A demonstration of the Lyman-α transitionin vacuum is useful to confirm whether the designed scheme works well and 2P-Ps behaves as
expected without the material eﬀects.
The components inside the chamber were modified to enable eﬃcient excitations of Ps in
vacuum. The sample holder was moved around 60 mm to downstream, and a multiple reflector
was installed ahead the holder. Figure 2.20 show a magnified view around the multiple reflector
and a detail description of the reflector. The lasers are reflected by mirrors (98 % reflectivity
for both UV and green) more than 20 times to fill the space of around 50 mm, which is a typicaldistance that Ps travels, along the positron beam axis. Ps is also confined in the vertical direction
to the lasers by silica wafers. Figure 2.21 shows an aligned path of the lasers. The picture wastaken from the side of the γ-ray detector. A weak green laser for the alignment was irradiated.
Multiple spots were observed at the mirror as the result of the multiple reflections. The UV laser
and the ionizing green laser were expanded into around 10 mm diameter outside the chamber toincrease the overlap with Ps. Ps can be always irradiated by the lasers while travelling in vacuum.
When the UV and the green laser are irradiated on this path, the intensity of annihilation
γ-rays detected in a largely delayed region increases because the dissociated positron by theionization is very slow to hit the surrounding materials. The typical distance to the surroundings
was 50 mm in the configuration to excite Ps in vacuum.

2.4 Gamma-ray detector
LaBr3 (Ce) scintillator (1.5 inch diameter, 2 inch length) was selected as the γ-ray detector because
LaBr3 (Ce) had a short decay constant of scintillation lights and good energy resolution. The
former merit enabled to discriminate signals from prompt decays and o-Ps decays, and thelatter to determine the decay mode of 2P-Ps in the material. The scintillator was coupled to
27

8

F

7

6

5

4

2

1

F

To be shown with magnified

Gamma-raydetector

6

E

3

5

4

Laser

E

D

D

C

10 cm

C

10 cm

Figure 2.19: Drawings of the setup to excite Ps in vacuum. (Left) Cross sectional drawing of thechamber. The lasers were reflected by two mirrors inside the chamber to be irradiated ahead of
the sample. Figure 2.20 shows magnified view around the sample. (Right) Drawing inside thechamber viewed from the downstream.

B

A

作成者

名前

日付

kshu

2019/12/12

B

A

確認者

Laser

Ps & laser reflector
8

7

承認者

6

Silica mirrors to reflect lasers
5

4

ForRombun

3

2

Uncapped aerogelm
55
Silica glass wafers
to reflect Ps

m

La
se
r

Figure 2.20: Multiple reflector for eﬃcient excitation of Ps travelling in vacuum. (Left) Magnified
view around the sample. (Right) Description of the multiple reflector. The lasers are reflected
more than 20 times to fill the space of around 50 mm, which is a typical distance that Ps travels.
Ps is confined in the vertical direction to the lasers by silica wafers.

28

1

1/1

A2

Magnified

Multiple spots of the laser

Uncapped aerogel
Mirror 1
Laser
Positrons

Mirror 2

Figure 2.21: Path of the lasers to excite Ps in vacuum. Multiple spots were observed at a mirror
as the result of the multiple reflections.
a HAMAMATSU R9869 photo multiplier tube (PMT). Figure 2.22 shows an averaged PMT
output waveform by detecting 511 keV annihilation γ-rays from the Na-22 radioisotope. The
waveform had the fast decay time constant of around 20 ns. Small dips appearing at around 65 ns
were generated by a reflection of the electric signal. The waveform was regarded as a responseof the detector. The response function was used in analysis as described in chapter 3. A function
to reproduce the waveform [49] is modeled as()
2∑(log((t − tk )/τ))2
R(t) =Vk exp −
.
(2.1)
2σk2
k=0
The components with k ≥ 1 represent the reflected signals. The parameters were determined byfitting to the waveform and summarized in Table 2.6. The reproduced function was superimposed
in Figure 2.22.
Energy resolution of the detector was evaluated by detecting γ-rays from Na-22. Figure 2.23
shows the energy spectrum and the estimated resolution. Deposited energy was estimated byintegrating waveforms. The energy dependent resolution was determined from resolutions of thepedestal and the two total absorption peaks to which Gaussian functions were fitted. High enoughresolution was obtained to clearly observe the valley of Compton free region (340 keV–511 keV)of 511 keV γ-rays. This performance was essential to discriminate decay modes of Ps between
2γ and 3γ modes.
Timing resolution of the detector was estimated by detecting both of the two 511 keV annihilation γ-rays of positrons from the beta decay of Na-22. Each γ-ray was detected by the adopted
γ-ray detector and a replicated one with the same type of the scintillator and the PMT. Figure 2.24
shows a spectrum of timing deference between total absorption signals of each detector. Arrival
timings of signals were estimated by that when passing a certain threshold level. The resolution
was estimated by fitting a Gaussian function to the spectrum and assuming both of the detectors
29

Height (V)

0.04

0.02

0
0

50

100

150
200
Time (ns)Figure 2.22: Response waveform of the γ-ray detector. Only total absorption events of 511 keVannihilation γ-rays were selected to generate the waveform. The response function which wasused in the analysis is superimposed.

Table 2.6: Parameters to reproduce the response waveform of the γ-ray detector.
τ

19.2 nsV00.0414 V

t0

1.43 ns

σ00.688 ns

V1

−0.0396V0

t1

52.4 ns

σ10.279 nsV2

−0.00598V0

t2

125 nsσ20.851 ns

30

Counts

6000

2000
4000
1000

4
10

3

2

4

Counts(arb.)Counts(arb.)

0c 2 / ndf
Prob
p0

1500

2.686 / 1
0.10130.003356 ± 7.615e- 07

1000

21

500

1
10-1

0

0

0

500 500

c2 / ndf
Prob
p0
p1

40

-0.02

0

0.02

0.04

0.361 / 1
0.548
1.873 ± 0.06867
8.8 ± 0.03743

20

0

1000
1000
Energy (keV)

-0.04

0

500

1000
g -ray energy (keV)

Figure 2.23: (Left) Energy spectrum by√ detecting γ-rays from Na-22. (Right) Estimated energy resolution. The function of σ = p0 E + p1 was fitted to estimate the energy dependent
resolution.

800
600

c2 / ndf

62.96 / 19

Constant

673.6 ± 9.6

Mean-1.741 ± 0.005

Sigma

0.412 ± 0.005

Counts (arb.)

00

6Integral
Resolution in FWHM (keV)0Counts (arb.)

1000
waveform (keV)

2000

400
c2 / ndf
Constant

300

Sigma

400

200

200

100

0

-3

-2
-1
0
Timing difference (ns)0Figure 2.24: Timing diﬀerence spectrum of the two detectors. A high enough resolution of
680 ps in FWHM was achieved.

31

Mean

-8

-6
Tch0
Peak - T

Figure 2.25: Input geometry in the Geant4 Monte Carlo simulation.
contributed in the same weight for the observed jitter. High enough resolution of 680 ps in
FWHM was achieved to measure the anticipated timing structure of γ-rays from decays of 2P-Ps.

2.5 Data acquisition system
Output waveforms of the γ-ray detectors and the photo detectors for lasers were recorded bya digitizer (National Instruments, PXIe-5162). High impedance terminals were used to record
large signals from γ-ray detector. A sampling rate was 1.25 GHz and a bandwidth 300 MHz forthe configuration. The signal from the γ-ray detector was recorded by two channels with diﬀerent
scales to record waveforms in a wide dynamic range with small quantization noises. The photodetectors were prepared for both of the UV laser and the green laser, and used to select data withor without each laser irradiation. Data acquisitions (DAQ) were triggered by logic trigger signals
from the positron beams of 50 Hz. A typical DAQ rate was 47 Hz as 94 % of the triggers.

2.6 Monte Carlo simulation
A Monte Carlo simulation was performed to estimate detection eﬃciencies of the γ-rays andenergy deposition spectra for each decay mode of Ps. Figure 2.25 shows a geometry input in the
Geant4 Monte Carlo simulator. Figure 2.26 shows obtained energy deposition spectra by eachmode of the decay. Mean deposition energies and total detection eﬃciencies are summarizedin Table 2.7.

32

Efficiency (/0.5keV)

10-2
10-3

3𝛾
10-4
10-5

2𝛾
0

200

400
Energy (keV)

Figure 2.26: Energy spectra of each decay mode by Monte Carlo simulation.

Table 2.7: Simulated detection eﬃciencies and mean deposition energies.
Decay mode

Mean deposition

Total eﬃciency

3γ

226 keV

4.11 %

2γ

272 keV

3.07 %

33

Chapter 3

Analysis Methods
This chapter describes analysis methods to measure decay rates of Ps. The decay rates were
estimated by data suﬀering from many pileups of annihilation γ-rays by the bunched positrons.
Typical output waveforms of the PMT are shown in Figure 3.1 by the full range, and in Figure 3.2
by the enlarged range. More than ten γ-rays were detected from the prompt decays, and the
majority of the delayed signals from o-Ps decays were piled up on others. Two methods wereadopted to be applied for the waveforms with such pileups. One analyzes averaged waveformsof the PMT output. This method is called Single-Shot Positron Annihilation Lifetime Spectroscopy (SSPALS) [50], which is expected to be robust for the pileups but yield only averaged
information. The other simply analyzes each single waveform to measure timings and heights ofeach γ-ray’s signal. A high-pass filter was applied on waveforms to reduce the pileup eﬀects inthis pulse-by-pulse analysis. This method can yield energy and timing spectra of each annihilation event while the applicable range is limited in a delayed region with less pileups. Proceduresof the methods are explained and validated through applications on data results of which were
expected. A phenomenological model to calculate intensities of annihilation γ-rays from appliedlaser field and the decay rate of 2P-Ps is also introduced. The decay rate of 2P-Ps is quantitatively
estimated by comparing predictions by the model with measured data.

3.1 Method based on an averaged waveform (SSPALS)
In the SSPALS method, waveforms are averaged over bunches of the positron beam, and thenthe averaged waveform is used as the target of the fitting. An expected waveform is generated byconvolving an assumed signal function with the response waveform of the γ-ray detector shownin Figure 2.22. A sum of squared residuals of each point, which are weighted by inverses ofvariances of each point, is minimized to estimate parameters in the assumed signal function.
The Monte Carlo method is adopted in this work to estimate statistical uncertainties and p-value
assuming Poisson distributions for detected numbers of events to take into account the correlation
between each point in the waveform.
35

Height (V)Height (V)

1

0.5

0.5

0

0
0

200

400

600
Time (ns)1Height (V)Height (V)

1

0.5

0

0
200

400

600
Time (ns)

200

400

600
Time (ns)

0

200

400

600
Time (ns)

1

0.5

0

0

Figure 3.1: Typical waveforms of the output of the PMT in the full range. More than ten γ-rays
were detected from the prompt decays.

36

Height (V)Height (V)

0.1

0.05

0.05

0

0
0

200

400

600
Time (ns)0.1Height (V)Height (V)

0.1

0.05

0

0
200

400

600
Time (ns)

200

400

600
Time (ns)

0

200

400

600
Time (ns)

0.1

0.05

0

0

Figure 3.2: Typical waveforms of the output of the PMT in the enlarged range. The majority ofthe signals were piled up on others.

373.2 Pulse-by-pulse analysis method
Energy depositions and timings of each detected γ-ray can be acquired by applying peak detections on each single waveform. This method is valid in a later timing region from the positron
irradiation where less annihilation γ-rays are piled up.
A high-pass filter was applied to waveforms in oﬄine to reduce the timing width of eachpulse and then to ease the distortion eﬀects by pileups. A simplified Wiener filter was chosen.
A characteristic function of the filter, H(ω), is formulated in Fourier space asH(ω) =

R(ω)∗,|R(ω)| 2 + |R(ωc )| 2

(3.1)

where R(ω) is Fourier transformation of the response function (Equation 2.1). ωc is a cut-oﬀ
angular frequency to suppress high frequency noises. ωc was determined to be 0.33 GHz to retain
the same level of signal-to-noise ratios as original waveforms. Figure 3.3 shows the adopted
characteristic function. The function was scaled so that signal amplitudes were not changed.
Performances of the filter were evaluated by data detecting γ-rays from Na-22. Figure 3.4
show comparisons of raw and filtered waveforms with various amplitudes. The time durationsof the pulses were narrowed to around 10 ns by the filter. Timings and heights of the peak points
were regarded as detected timings and energy depositions of γ-rays with setting an appropriate
threshold.
Linearity and energy resolution were checked by comparing with values yielded from analyzing raw waveforms. Figure 3.5 show a correlation of estimated energy depositions and energy
spectra by Na-22. Peak heights of filtered pulses were proportional to energy depositions whichwere evaluated by integrating raw waveforms. The energy resolution shown in Figure 3.6 wasstill good enough to clearly observe the valley of Compton free region (340 keV–511 keV) of
511 keV γ-rays. This good resolution would enable to discriminate decay modes of Ps between
the 2γ and 3γ modes.
A timing resolution was evaluated in the same way as section 2.4. Figure 3.7 shows timing
spectra of the peaks. The good timing resolution of 640 ps in FWHM was achieved with a tiny
time walk eﬀect over 150 keV. The resolution of the reference detector (680 ps FWHM) was
subtracted to evaluate the contribution from the single detector.

3.3 Quality check of analysis
Analyses were applied on data acquired by using the bunched positrons to check qualities of themethods. All of the data analyzed here were acquired without irradiating any lasers. The twoanalysis methods were confirmed to yield the expected decay rates and production probabilities
of 1S-Ps, and energy distributions of annihilation γ-rays from 1S-Ps decays. In this section,
statistical uncertainties are quoted on estimated parameters.
38

|H(w)|

105
104

No cutoff
With cutoff 𝜔" = 0.33 GHz

102
1
10-2

Arg(H(w))

10-4
10-2

10-1

1
w (GHz)

10-2

10-1

1
w (GHz)20-2

Figure 3.3: Magnitude (top) and argument (bottom) of the characteristic function of the high-passfilter39

Raw
Filtered0.1

Signal amplitude (V)Signal amplitude (V)0.15

510 keV0.05

01270 keV
0.1

0.05

0
0

100

200
Time (ns)0.150Signal amplitude (V)Signal amplitude (V)0.15

790 keV
0.1

0.05

0

100

200
Time (ns)0.15

240 keV
0.1

0.05

0
0

100

200
Time (ns)

0

100

200
Time (ns)Figure 3.4: Comparison of raw and filtered waveforms. The time durations of the pulses were
narrowed by the filter from 30 ns to 10 ns in FWHM.

Figure 3.5: (Left) Correlation between filtered pulse peak heights and energy deposition estimatedby integrating raw waveforms. (Right) Energy spectra. Good enough linearity and resolution
were achieved.

40

b

stant

an
ma

Resolution in FWHM (keV)100

χ2 / ndf
Prob
p0
p1

5.377 / 1
0.020415.896 ± 0.2206
574.7 ± 2.437

50
χ2 / ndf
0.361 / 1
Prob
0.548
p0
1.873 ± 0.06867
p1
8.8 ± 0.03743

0

0

500

1000
Energy (keV)

Figure3.6: Energy resolution of filtered waveform analysis. The fitted functions were√p0 × Energy + p1. The resolution is good enough to discriminate a decay mode of Ps.

2094 / 117
0475.7 ± 9.9-1.578 ± 0.009
0.7854 ± 0.0146

0ch1
es - TThres (ns)Counts (arb.)

ndf

FilteredRaw

c2 / ndfProb

29.49 / 37
0.8055Constant
492.9 ± 5.9
Mean-6.358 ± 0.005
Sigma
0.4339 ± 0.0049

400

200

0

-8

-6
-4
Peak timing (ns)Figure 3.7: (Left) Timing spectrum of the filtered pulses’ peak. (Right) Correlation between
heights and timings. The timing resolution was as good as that evaluated by the raw waveforms.

41

3.3.1 Decay rate and production probability
Application of the Ps decay modelTime dependent intensity of annihilation γ-rays, S(t), is modeled to deduce decay rates andproduction probabilities of o-Ps in 1S state. The model was formulated as( ∫ t)S(t) = ε2 Nprompt δ(t) + (ε2 Γpo (t) + ε3 Γs )NoPs exp −(Γpo (t ′) + Γs )dt ′ .
(3.2)
0

The first term represents the prompt decay of p-Ps or positrons which do not form Ps. Thosecomponents generate annihilation γ-rays in less than 1 ns, which is considered to have the delta
functional spectrum for the measurement system in the present work. The second term represents
the signal from decays of o-Ps. As for meanings of the symbols, εn are detection eﬃciencies ofnγ decay. Γs and Γpo are decay rates of the self decay and the pick-oﬀ decay of o-Ps respectively.
Γpo may depend on time by the thermalization process. Nprompt and NoPs are produced numbersof each component. The production probability can be calculated as 43 NoPs /(NoPs + Nprompt )considering the spin statics. The detection eﬃciencies are multiplied by the simulated meanenergy depositions when combined with the SSPALS analysis.
In the SSPALS analysis, the time profile of the positron beam was treated in diﬀerent ways
to be combined with the decay model. For the prompt decay component, the waveform acquiredwith the kapton target was used without being convolved with the response function, because theprompt decay was the dominant component in the kapton target. Nprompt and a timing of the pulse
were set to be free parameters in the fitting. For the o-Ps component, a time profile of the positron
beam was assumed, and then was convolved with the model function. The timing profile wasassumed to be a convolution of the beam timing profile in short time duration (Figure 2.3) and a
Gaussian function which could have diﬀerent widths for both sides. The Gaussian function wasused for modeling a timing jitter of the positron beam during data acquisition duration, which was
typically ten minutes. The widths were determined to reproduce the waveform acquired with thekapton target by convolving the beam timing profile and the response of the detector. Figure 3.8
shows the assumed timing profile, and compares the kapton waveform with the reproduced one.
The origin of the timing was determined so that the waveform with the kapton started from theorigin. One sigma widths of the jitter function were determined to be 1.0 ns in negative and13.7 ns in positive. The convolved timing profile was used hereafter in the SSPALS analysis.
A systematic uncertainty from this assumption is estimated by adopting wider and narrower
profiles. The wider profile was determined to include the whole kapton waveform. The shorttime duration profile was used as the narrower profile.
Applying SSPALS analysis
The SSPALS analysis was applied on data using silica aerogels as targets and the parameters
was confirmed to be consistent with other measurements described in section 2.2. Figure 3.9
shows results of fitting the reproduced waveform to a measured waveform by the capped aerogel.
The waveform was reproduced well by the SSPALS analysis. The production probability wasestimated as 26.9 ± 0.6(stat.) % , which reasonably agreed with the other measurement described
42

0.06

Reproduced waveform

0.04

0.08

Convoluted
Short duration profile

0.06

Jitter function

0.04
0.02

0
0

50

100

0
-20

150
200
Time (ns)

0

20

40
Time (ns)1Height (V)Height (V)Figure 3.8: (Left) Comparison between the kapton and reproduced waveform. (Right) Assumed
timing profile of positron beam. One sigma widths of the jitter function were 1.0 ns in negative
and 13.7 ns in positive.
MeasuredgWfmAveCombined_ch0;Time (ns);Height (V)Fitted(sum)
gFitProfile
gSig_0;Time(ns);Height (V)Fitted (prompt)
Fitted(oPs)
gSig_1;Time(ns);Height (V)10-1

𝑁123415 = 1631 ± 5
𝑁3<= = 413 ± 9
𝑝-value = 0.30

10-2

Measured − Fitted (sum)

0.001

0
-0.001

10-3
0

200

400

600
Time (ns)

0

200

400

600
Time (ns)Measured (Pulse-by-pulse)(SSPALS)
Expected thermalizationMeasured
with L=34nm

30.2

Measured (Pulse-by-pulse)

1

2

0.1
1
0.5
0
00

certainty

ion

y measured pick-off decay rates

Ps kinetic energy (eV)600Time (ns)

1.5
0.08
1

0.06

0.04
0.5

200200400 400 600 600
Time (ns)Time (ns)

0

200

400
600
Time (ns)Figure13.10: Pick-oﬀ decay rates in the capped aerogel1by the SSPALS analysis. The expected
0.4 by the thermalization process described in section 1.1.2, and a result from the pulseevolutions
by-pulse analysis are superimposed. The right figure is the enlarged view of the left.
Range of uncertainty

Best estimation

Estimated by measured pick-off decay rates

0.3

0.5
0.2

43

0.5

0.1
600
Time (ns)Ps kinetic energy (eV)Measured (SSPALS)

G2 (µs-1)

1.5
4

Ps kinetic energy (eV)G2 (µs-1)G2 (µs-1)

Figure 3.9: (Left) Measured and fitted waveforms. The fitted waveforms and intensities of eachcomponent in the decay model are superimposed. (Right) Residuals of the fit.

ed (Pulse-by-pulse)0

Kapton waveform

0.02

ed (SSPALS)

400

Height (arb.)

Height (arb.)

´10-3

00

200
200

400
400

600
600
Time (ns)

0

200

400

600

Height (V)Height (V)1

gWfmAveCombined_ch0;Time(ns);Height (V)MeasuredgFitProfile
Fitted (sum)gSig_0;Time(ns);Height (V)Fitted (prompt)
gSig_1;Time
Fitted(oPs)(ns);Height (V)10-1

𝑁"#$%"& = 1470 ± 5
𝑁$./ = 486 ± 9
𝑝-value = 0.0005

Measured − Fitted (sum)

0.001
0

10-2

-0.00110-3-0.002
0

200

400

600
Time (ns)

0

200

400

600
Time (ns)Measured (SSPALS)
Measured (Pulse-by-pulse)

4

4
0.1

Measured (SSPALS)
Measured (Pulse-by-pulse)

0.053

Assumed ( - 40ns)
Expected (40ns - )

1.5

1

02
2

G po (µs-1)-1)
G po ((µ
µss-1
G
)
po

G po (µs-1)

Figure 3.11: (Left) Measured and fitted waveforms. The fitted waveforms and intensities of eachcomponent in the decay model are superimposed. (Right) Residuals of the fit.

-0.05
1

0
0

200

400

600
Time (ns)

-0.1
0
00

0.5
200
200

400
400

600
600
Time
Time(ns)(ns)

Figure 3.12: Pick-oﬀ decay rates in the uncapped aerogel by the SSPALS analysis. A result fromthe pulse-by-pulse analysis is superimposed. The right figure is the enlarged view of the left.
in section 2.2. The estimated pick-oﬀ decay rates were shown in Figure 3.10. The timing region
was divided into four parts (0 ns–50 ns, 50 ns–120 ns, 120 ns–240 ns, and 240 ns–600 ns), and thepick-oﬀ rates at each start time of the regions were set to be free parameters. The rates insideeach time region but the last one were assumed to be linear functions. In the last region, therate was set to be constant. The rates after 50 ns were consistent with the expected function by
the thermalization process described in section 1.1.2. The mean free path to draw the expectedfunction was estimated to be 34 nm to reproduce the thermalized pick-oﬀ decay rate. Whenestimating the thermalization process, kinetic energy of Ps was averaged over the timing profileof the positrons. In the first time region, the result would not be so reliable and mainly determinedby the linear constraint from the second region because a systematic error should be large dueto the large amplitude from prompt decays. The NoPs and the first decay rate were strongly
correlated each other.
The results for the uncapped aerogel were shown in Figure 3.11 and Figure 3.12.
Thehigher production probability as 33.0 ± 0.6(stat.) % was obtained without the cap because morepositrons stopped in the pore network of the aerogel. The pick-oﬀ rate at well thermalized
440Signal amplitude (V)

0.2
0.1
0
-0.1

Signal amplitude (V)Raw
Filtered
Detected peaks

200

400

0.3
0.2
0.1
0
-0.1

200

400

0.3
0.2
0.1
0
−0.1

600
Time (ns)Signal amplitude (V)Signal amplitude (V)

0.3

600
Time (ns)

200

400

600
Time (ns)

200

400

600
Time (ns)

0.3
0.2
0.1
0
-0.1

Figure 3.13: Filtered waveforms and detected peaks in the pulse-by-pulse analysis. A lot of
pileups were removed and the simple process to detect peaks was valid.

timing was consistent with zero as expected from the observation that o-Ps escaped into theouter vacuum of the pores without the cap. In conclusion, the SSPALS analysis was able toquantitatively measure properties of o-Ps in most of the timing regions.
Applying pulse-by-pulse analysis
The pulse-by-pulse analysis was also applied to the same data. Typical waveforms on which thehigh-pass filter was applied, and detected peaks are shown in Figure 3.13. Waveforms recordedin the enlarged range were used in the pulse-by-pulse analysis to avoid large quantization noises.
A lot of pileups were removed after around 200 ns where the tails of the large signal from theprompt decays became small. The simple process to detect peaks was valid for the filteredwaveforms.
The thermalized pick-oﬀ rates were estimated by fitting the o-Ps decay model to timing
spectra shown in Figure 3.14. Pulses with more than 240 keV energy deposition were includedin the spectra to reject fake peaks by noises or ringing side peaks. The rates were assumed to beconstant in the fitting region (240 ns–1200 ns), and are shown in Figure 3.10 for the capped andFigure 3.12 for the uncapped. Both results were consistent with those from the SSPALS analysis.
45

Counts (/10ns /bunch)1
Without cap
𝑁"#$ = 422 ± 7
Γ+ = 0.006 ± 0.05 𝜇s 34
𝜒 + ⁄𝑛𝑑𝑓 = 177/94

-1

10

10-2
With cap
𝑁"#$ = 407 ± 8
Γ+ = 0.64 ± 0.07 𝜇s 34
𝜒 + ⁄𝑛𝑑𝑓 = 187/93

10-3
10-4
0

500

1000
Time (ns)Figure 3.14: Timing spectra of o-Ps decays through the pulse-by-pulse analysis. The fitting
yielded the consistent estimations with the SSPALS analysis as shown in Figure 3.10 and Figure 3.12.
NoPs with the cap agreed between the both methods, but without the cap 15% less number was
estimated in the pulse-by-pulse analysis compared with the SSPALS analysis. There would be
systematic errors originating from an extrapolation of the model function to t = 0, which wasan unavoidable procedure in this pulse-by-pulse analysis due to the large pileups at the prompt
region. For example, annihilations in early timing, such as decays of very fast Ps hitting walls of
the chamber, were not able to be detected in the pulse-by-pulse analysis to result in estimating
the less number of Ps. Errors from the extrapolation would be evaluated when estimating the
decay rate of 2P-Ps.
When estimating the uncertainty of the parameters, statistical uncertainties of each bin werescaled for the reduced chi-square to be unity. The poor goodness-of-fit would be attributed toresidual pileup eﬀects.
The gain by the high-pass filter can be confirmed by comparing the timing spectrum with that
produced by simple processes to detect timings of rise-ups in the waveform without the filter.
The timing spectra for the aerogel with the cap are compared in Figure 3.15. Both spectra agreed
after around 600 ns where less pileups occurred, but less signals were detected without the filterin the earlier timing. A spuriously longer lifetime than that of o-Ps in vacuum was obtained byfitting the decay model to the spectrum which eﬀectively had the less detection eﬃciency. The
high-pass filter worked well to ease the pileup eﬀects and obtain the physical and reasonable
decay rate of Ps.

3.3.2 Energy of gamma-rays from Ps decay
An energy spectrum of γ-rays from Ps decay was produced through the pulse-by-pulse analysis
and compared with the Monte Carlo simulation to validate the analysis method. Figure 3.16
shows the measured and simulated spectra for the aerogel with the cap. Pulses detected after46

Counts (/10ns /bunch)With the high-pass filter

1

Without the filter

10−1
10−2
10−3
10−4
0

500

1000
Time (ns)Counts (/4keV /bunch)

Figure 3.15: Comparison of timing spectra with and without the high-pass filter. Without thefilter, less signals were detected in 200 ns–600 ns due to the pileups.

Measured
Simulation (2γ )0.01

Simulation (3γ )Simulation (Sum)

0.005

0
0

200

400

600
800
Energy (keV)

Figure 3.16: Energy spectrum of annihilation γ-rays from o-Ps by the pulse-by-pulse analysis.
The spectrum reasonably agreed with the MC simulation, whose mean deposition energy was
diﬀered by only 2 % with the measurement. The pulse-by-pulse analysis had the good sensitivity
to distinguish the decay modes of Ps. The deviation of the mean deposition energy is considered
to be the magnitude of the systematic uncertainty.

47

400 ns were collected in the spectrum. The simulated 2γ and 3γ spectra were added according
to branching ratios of each decay mode, which were determined by the thermalized pick-oﬀ rate,
and then scaled. A good agreement between the measurement and the simulation was observed.
The pulse-by-pulse analysis is expected to have good enough sensitivity to distinguish the decay
modes of Ps.
A discrepancy of the mean deposited energies between the measurement and the simulation
was 2 %. This value is used to evaluate the systematic uncertainty from the MC simulation.

3.4 Model of excitation and decay of 2P-Ps
3.4.1 Equations of internal states
A new formalization is introduced in order to quantitatively estimate the decay rate of 2P-Ps. The
decay rate is included in the following optical Bloch equations [51], by which a density matrixof the Ps internal states under the irradiation of the UV laser evolves.
diρ11 = Ω(ρ12 − ρ21 ) − Γ1 ρ11 + (Γsp + P1 Γ2 )ρ22,
dt
2
(
)
d ∗
i
1
d
ρ12 = ρ21 = Ω(ρ11 − ρ22 ) + i(ω21 − ω L ) − (Γ1 + Γsp + Γ2 ) ρ12,
dt
dt
2
2
i
d
ρ22 = − Ω(ρ12 − ρ21 ) − (Γsp + Γ2 )ρ22 .
dt
2

(3.3)
(3.4)
(3.5)

An intensity of annihilation γ-rays from the decay can be calculated by the density matrix. Theseequations are numerically solved with inputting parameters of the laser, and then the decayrate of 2P-Ps will be estimated by fitted to measured timing spectra of the annihilation γ-rays.
Definitions of the symbols are as follows:
ρi j : Elements of the density matrix. ρi j = ci∗ c j where ci is a probability amplitude of n = istate.
ω21 : Resonant angular frequency of the Lyman-α transition.
Γ1 : Annihilation decay rate of the 1S state. This is the sum of the self decay rate and thepick-oﬀ decay rate of o-Ps.
Γsp : Spontaneous decay rate of the 2P state.
ω L : Angular frequency of the irradiated laser.
Ω: Rabi frequency determined by electric field of the laser.
Γ2 : Decay rate of 2P-Ps in the material.
P1 : Branching ratio of a process in which a dissociated positron forms 1S-Ps.
48

Γ2 is the target quantity to be estimated, and P1 is also phenomenologically introduced to describe
a possible process in the material. 2P-Ps is modeled to be dissociated into a positron and anelectron with the rate of Γ2 . The dissociated positron would form 1S-Ps again with a probabilityof P1 , and the remained is assumed to decay into annihilation γ-rays. It would be possible to set
a physical limit on P1 from around 0.2 to 0.4, which is an assumed range of the o-Ps production
probability inside the silica aerogel used in the present work. P1 was assumed to be 0.3 according
to measurements of production probabilities of o-Ps in the present work.
A total increase of the decay rate of Ps by the laser irradiation can be calculated by a following
expression:ρ11 (t)Γ1 + ρ22 (t)(1 − P1 )Γ2
ΓL (t) =− Γ1 .
(3.6)
ρ11 (t) + ρ22 (t)Time dependent intensity from decays of Ps can be formulated by adding ΓL (t) to Equation 3.2
as
S(t) =ε2 Nprompt δ(t)( ∫ t)(Γpo (t ′) + Γs + ΓL (t ′))dt ′ .
+ (ε2 Γpo (t) + ε3 Γs + ε L ΓL (t))NoPs exp −

(3.7)

0

ε L is the detection eﬃciency for γ-rays from the decays of 2P-Ps. The decay mode of 2P-Ps willbe also inspected.

3.4.2 Predictions by the modelΓL (t) can be calculated by inputting modeled laser fields. Rabi frequency Ω depends on theelectric field of the laser, and Ω determines the excitation eﬃciency. Ω can be calculated asΩ(t) = e ⟨2P|r |1S⟩ E(t)/ℏ, where e ⟨2P|r |1S⟩ is a dipole moment evaluated in an overlap of the
wave function of each state, and E(t) is an envelope of the electric field of the laser. E(t) wasmodeled by Fourier transform of a multi-mode Gaussian spectrum Ẽ(ω):
))
(
)
(
(
∆2ω
E0 ∆ω
t2
∆ω t
E(t) =
ϑ3, exp − 2 exp − 2 ,
2π σω
2
2σω
2σt
)
)
(
(
∞
2
∑
1
σt
(k∆ω )(ω − k∆ω )2∆ω √.
Ẽ(ω) = E0exp −√ exp −
2(1/σt )2
2σω2
2πσω
2π
k=−∞

(3.8)
(3.9)

ϑ3 (z, τ) is the elliptic theta function, E0 amplitude of the field, σω band width, σt time durationof pulse, and ∆ω interval of the modes. Here 1/σt becomes a band width of each mode. σtand σω were set to reproduce the timing profile and frequency spectrum of the UV laser. E0
was determined according to the pulse energy and the beam diameter of the laser, and averaged
over the spacial profile of the positrons. ∆ω was assumed to be 2π×1.0 GHz by a length of
the resonator in the OPO laser. Figure 3.17 show a calculated timing profile and a frequency
spectrum using σt = 3 ns and σω = 2π × 64 GHz. By squaring the field amplitude to get thepower profile, it can be confirmed that the measured time duration of the pulse (5 ns) and band
width (1.1 × 102 GHz) as described in subsection 2.3.1 were reproduced.
49

Figure 3.17: Simulated laser field. (Left) timing profile. (Right) Frequency spectrum. The
power profile and spectrum can be obtained by squaring the field amplitudes to be comparedwith the measured pulse time duration and the band width.

(a) ρ11 element.

(b) ρ22 element.

Figure 3.18: Example of density matrix by the model calculation of the Ps excitation.
An example of the calculations based on the model is shown in Figure 3.18 for the density
matrix elements, and Figure 3.19 for ΓL , which is the increased intensity of annihilation γ-raysby the enhanced decay. The envelope of ΓL has a Gaussian timing profile with the same width
as the laser power profile. Here the integration of the increased decay rate was defined to be I L .
ΓL can therefore be formulated as()
t − tLIL
exp −.
(3.10)ΓL (t) = √
2σL2
2πσL
t L represents timing of irradiation of the laser, and σL is a width of the profile. Probability for
Ps to decay by laser irradiation can be calculated as 1 − exp(−I L ) by this parametrization. I L andcorresponding probability to decay are calculated for various wavelengths of the laser and Γ2 asshown in Figure 3.20. Broad resonance spectra with the natural line width were reproducedby the model. Resonance spectra were modeled by Voigt functions, which were convolutions ofGaussian and Breit Wigner functions, to be used in analysis. ΓL linearly depended on the pulse
energy and 1 − P1 . These dependence are used to estimate systematic uncertainties.
50

15
10
5

0

0

L

IL

Γ2=33333GHz
Γ2=10000GHz
Γ2=2857GHz
Γ2=1667GHz

Decay prob. [ 1.0 - exp(-I ) ]Figure 3.19: Example of ΓL by the model calculation of the Ps excitation.

0.5
1
1.5
Wavelength detune (nm)

Γ2=33333GHz
Γ2=10000GHz
Γ2=2857GHz
Γ2=1667GHz

1.0

0.5

0.0

0

2

4
6
8
Wavelength detune (nm)Figure 3.20: Resonance spectra of integrated decay rate I L (left) and corresponding probability
to decay (right). The points were results of the calculations, and the curves were modeled Voigt
functions to be used in analysis. Broad resonance spectra with the natural line width werereproduced by the model.

51

Chapter 4

Results and discussion
Results of the measurements of the decay rate of 2P-Ps (Γ2 ) confined in the pores are reported
and discussed in this chapter. In contrast to be in vacuum, the enhanced decay and the broadresonance spectrum were observed in the silica aerogels’ pores where 1S-Ps did not form thesurface state. This observation favors that some of the distinctive features of the 2P state induce
the abnormal phenomena. Γ2 was measured to be in the order of 1 THz in the measured rangeof Ps kinetic energy (0.04 eV–0.2 eV). The decay rate can be interpreted as the decay process
occurred in almost every collision with the material, and had a resonance around Ps kinetic
energy of 0.06 eV. The broadening was observed independently on Γ2 as wide as around 1 nm in
FWHM. Possible mechanisms of the broadening and the enhanced decay, and future directionsof studying them are discussed.

4.1 Demonstration of Ps Lyman-α transition in vacuum
The Lyman-α transition of Ps in vacuum was demonstrated to confirm that the system was able
to excite Ps into the 2P state and then ionize it to detect annihilation γ-rays from the dissociatedpositron. The silica aerogel without the cap was used to let o-Ps escape in the outer vacuumof the pores, and the UV excitation laser and the green ionization laser were irradiated on theescaped o-Ps.
Annihilation γ-rays from the dissociated slow positrons were observed in a largely delayed
timing region. Figure 4.1 show the timing spectra and energy spectra of the delayed γ-rays
emitted after 700 ns from the irradiation of the positrons. The wavelength of the UV laser was
set to be 243.0 nm for this measurement. An intensity of the very slow component after around1000 ns increased by the laser irradiations because the dissociated positrons were so slow to takesuch a long time to hit the surrounding materials. The decay mode of the slow component was
confirmed to be the 2γ mode from the 511 keV total absorption peak in the energy spectrum. Thisagreed with the expected poor production of the long lived o-Ps in the majority of surrounding
materials of the chamber.
The transition signal was not observed without the green laser, or with detuned wavelengthsof the UV laser. The timing spectrum by irradiating the UV laser alone is shown in Figure 4.2,
and the signal of the transition scanned against wavelength of the UV laser is shown in Figure 4.3.
53

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

No laser No laserWith UV and
With
Green
UV andlaser
Green laserCounts(/10keV/bunch)Counts(/1mv /bunch)

1

Counts (/1mv /bunch)

Counts (/200ns /bunch)

Counts (/200ns /bunch)1

No laser0.008 0.008

No laserWith UV andWith
GreenUV laserand Green laser

0.006 0.006
0.004 0.004
0.002 0.002

10-5 10-500 2000 2000
4000 4000
6000 6000
Time (ns)Time (ns)

0
0

0
0

200 200

400 400 600 600
HeightHeight(V) (keV)(V)
EnergyFigure 4.1: Timing (left) and energy (right) spectra of annihilation γ-rays from Ps excited in
vacuum. An intensity of the very slow component after around 1000 ns increased by the laser
irradiations. The decay mode of the slow component was confirmed to be the 2γ mode as
expected.
The lack of the signal without the green laser and the resonance at 243 nm are good evidencesof the successful demonstration of the designed processes in which the laser irradiations induced
Ps Lyman-α transitions and the following ionizations.
A Gaussian function was fitted to the resonance spectrum, and the width was 0.21 nm in
FWHM. Assuming that the width was from Doppler broadening, the mean kinetic energy ofPs was estimated as 0.20 eV, which corresponded to 1.5 × 103 K. The energy was reasonablefrom the expected thermalization process as shown in Figure 3.10. The enhanced decay and thebroadening were not observed if Ps was excited in vacuum.

4.2 Observation of the enhanced decay and the broadening for confined 2P-Ps
The enhanced decay of Ps into annihilation γ-rays was observed by irradiating the UV laser
alone on Ps confined in the aerogel with the cap. Figure 4.4 shows waveforms of the PMT
outputs with and without the UV laser irradiation, and the diﬀerential waveform. Only UV
laser (485 µJ pulse energy at the sample, 243.0 nm wavelength) was irradiated at 310 ns delayed
from the positrons. An instance increase of the annihilation γ-rays was observed just after thelaser irradiation. γ-rays emitted after around 370 ns decreased because less 1S-Ps remained. The
enhancement of the decay was so strong that around 50 % of Ps decayed as obvious from a timing
spectrum by the pulse-by-pulse analysis, which is shown in Figure 4.5. The energy thresholdof 240 keV was set to produce the spectra. The increase of the annihilation γ-rays at the timingof the laser irradiation was also observed, and the intensity after the increase became around thehalf of that without the laser. In the following subsection 4.2.2, the timing profile of the γ-rays
enhanced by the laser and the quantitative consistency between the increased and the decreased
54

10-1

Counts (/1mv /bunch)

Counts (/200ns /bunch)

No laser1

Only UV laser

10-2

0.005

0.004

10-3

0.003

10-4

0.002

10-5

0.001

0

2000

4000

6000
Time (ns)

0
0

100

200

300

400

500

600

700

800

´10-3
0.15

c 2 / ndf

44.44 / 8

Const

0.0001416 ± 3.631e- 06

s (nm)l 0 (nm)

0.08778 ± 0.002041
243 ± 0.003001

UV and Green

0.1

Only UVNOn - NOff
(6µs-1 bunch-1 µJ-1)
UVEnergy

NOn - NOff
(6µs-1 bunch-1 µJ-1)
UVEnergy

Figure 4.2: Timing spectrum by irradiating only UV laser on Ps in vacuum. The increase of thedelayed component was not observed.

´10-3
c 2 / ndf
Prob
Const
s(nm)
l (nm)

0.06

0

0.05
0.04
0.03
0.02

0.05

0.01

0
242.6 242.8

243243.2 243.4
Wavelength (nm)

0

242.6
242.7
242.8
242.9243243.1
243.2
243
WavelenFigure 4.3: Resonance spectrum of Ps Lyman-α transition in vacuum. The center of the resonance
was reasonable for the Lyman-α, and the width agreed with that of Doppler broadening bytemperature of 1.5 × 103 K, which can be reasonably assumed from the thermalization process.

55

Height (V)Height (V)

1

10-1

With the laser (A)Laser irradiation timing
A − (B)
0.006
0.004

Without the laser (B) 0.002

10-2

0
0

200

400

-0.002600
Time (ns)

0

200

400

600
800
Time (ns)Figure 4.4: (Left) Waveforms with and without the UV laser. (Right) Diﬀerential waveformgenerated by subtracting the waveform without the laser from that with the laser. Annihilation
γ-rays were increased just after the laser irradiation.

1

Without laserWith laser

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

± stat. ± (sys. )𝜒 2/𝑛𝑑𝑓

104/72

𝑁𝑜𝑃𝑠 at 296 ns

25.8 ± 0.6 ± 0.5

Parameters from the MCΓ𝑝𝑜

0.8 ± 0.1 ± 3×10 −6 𝜇s−1

𝜀D over 240 keV 1.59 ± 0.04 %𝐼𝐿

0.74 ± 0.03 ± 0.04

𝜀L over 240 keV 1.47 ± 0.03 %𝜎𝐿

1.05 ± 0.04 ± 0.003 ns

Counts (/0.4ns /bunch)

Counts (/10ns /bunch)

Result of the fitting

Without laser

0.03With laser

0.02

0.01

0
0

500

1000
Time (ns)

300

310

320
Time (ns)Figure 4.5: Timing spectra of the γ-rays increased by the UV laser. (Left) In a long time range.
(Right) Focused at the laser irradiation timing. γ-rays enhanced by the laser were emitted bypulse shaped timing profile. The spectra were fitted by the decay model to yield parameterssummarized in tables in the figure. The reproduced curves are superimposed.

56

1

23.96 / 90.004361
0.9046 ± 0.08714
243.1 ± 0.01886
0.3604 ± 0.02202

0.5

c2 / ndf

0.6

Const
l0(nm)0s (nm)

0

0.4
0.2
0

0
235

Integrated decay rateILc2 / ndf
ProbConst
l 0(nm)
s(nm)

240
245
250
Laser wavelength (nm)

242

242.5

Figure 4.6: Resonance curve of I L in wide range of wavelength. The enhanced decay had theresonance at Ps Lyman-α (243 nm) and the width was broad as 0.8 nm in FWHM. Doppler
broadening or the collisional broadening was not able to naively explain this broad width by thereasonable kinetic energy of Ps.
intensity are studied in detail by applying the decay model of Ps in section 3.4.
The enhanced decay was observed at the resonance of the Lyman-α, and the width was
also broadened as observed in the previous work [2]. Figure 4.6 shows a dependence of I L
scanned in a wide range of wavelength of the UV laser. I L were estimated so that 1 − exp(−I L )represented the decayed ratio of Ps by the UV laser. The enhanced decay had the resonance at
Ps Lyman-α (243 nm). This feature of the resonance favors that the UV laser induced Lyman-αtransition rather than active centers, which could quench Ps, on the pore surface of the aerogels,because the silica aerogels did not have a resonance structure at the wavelength of Ps Lyman-α inlight absorption spectra as described in subsection 2.2.6. The resonance spectrum was fitted by aGaussian function to estimate the width as broad as 0.85 nm in FWHM. The width was too broad
to be naively attributed to Doppler or the collisional broadening. The mean kinetic energy of Ps
to explain the broad width by those eﬀects is more than 3 eV, which is not consistent with thethermalization process in the aerogel. The broadening should be caused by other eﬀects inducedby the material.
From the above observations, it was concluded that even in the aerogel the decay of 2P-Ps
was enhanced and the resonance spectrum was abnormally broadened. Because the lifetime of
1S-Ps in the aerogel agreed with the prediction of the RTE model, it was expected that 1S-Ps did
not form the surface state. The mechanisms of the enhanced decay and the broadening should be
related to some of the distinctive features of the 2P state. Measurements of the dependences on Ps
kinetic energy of the enhanced decay rate and the broadening are reported in section 4.3, which
will be useful to identify physical mechanisms. The dependences were measured by scanning
the timing of the irradiation of the UV laser. The kinetic energy was estimated to be ranged in
0.04 eV–0.2 eV as shown in Figure 3.10. The following subsections discuss the decay mode of57

243 243.5
Laser wavelen

Counts (/7.5keV /bunch)With laser
No laser
Simulation (2γ )Simulation (3γ )Simulation (Sum)

0.008
0.006
0.004
0.002
0
0

200

400

600
Energy (keV)

Figure 4.7: Energy spectra of γ-rays emitted around the laser irradiation. Because the total
absorption peak of 511 keV γ-rays was clearly observed for the enhanced decay by the UV laser,
it was assumed that the decay of 2P-Ps was fully in the 2γ mode.
2P-Ps and the application of the decay model, which are used in the quantitative analysis.

4.2.1 Decay mode of the confined 2P-Ps
A dominant decay mode of the confined 2P-Ps was confirmed to be the 2γ mode from an energy
spectrum of γ-rays enhanced by the laser. Figure 4.7 shows energy spectra of γ-rays detected
in a ±3 ns timing region around the laser irradiation. The total absorption peak of 511 keV
γ-rays was clearly observed for the enhanced decay by the UV laser. Higher energy signals than
the total absorption might be recorded due to the residual pileups, which could also cause thedisagreement of spectra between the measurement and the simulations. The decay mode of theconfined 2P-Ps was assumed to be in fully 2γ mode hereafter.

4.2.2 Adaptability of the decay model
Adaptability of the decay model of Ps described in section 3.4 was confirmed by applying themodel to measured data. First, the timing profile of the enhanced γ-rays is inspected. In theright of Figure 4.5, the fitted model function is superimposed on the timing spectrum. Whilefitting to the data with laser, NoPs and Γpo were fixed by those acquired from the data withoutlaser. The laser enhanced γ-rays were confirmed to have a pulse like shape, which originatedfrom the timing profile of the pulse laser as expected by the model. The timing width of thelaser enhanced decay, σL , was estimated as σL = 1.05 ± 0.04(stat.) ± 0.003(sys.) ns, which was
2.47 ± 0.09(stat.) ± 0.007(sys.) ns in FWHM. Here the systematic uncertainty from the MC simulation is quoted. The width was much wider than the achieved timing resolution (0.64 ns FWHM)
described in section 3.2. The contribution from an intrinsic timing profile of the enhanced decay
was estimated as 2.39 ns by subtracting the resolution. This width reasonably agreed with thepossible pulse duration of the UV laser, which is explained in section 2.3. The model was able
to describe the timing profile of the laser enhanced γ-rays.
58

Result of the fitting

0.20

N,-./,01675 ± 2 ± 76

MeasuredFitted (sum)Fitted (prompt)
Fitted (oPs)

10-1

N.67

346 ± 1 >?
;<=𝜀N

9.3 ± 0.4 keV

Γ𝑝𝑜 after 240 ns

1.13 ± 0.07 ± 0.02 𝜇s −1

𝜀L

8.4 ± 0.4 keV

𝐼𝐿

0.72 ± 0.03 >K.K<;K.KL

Height (V)Height (V)Parameters from the MC1± stat. ± (sys. )𝑝-value

Measured (Laser on - off)
Fitted (sum)Fitted (increased)

0.005

Fitted (decreased)

10-2
0
10-3
0

200

400

600
Time (ns)

0

200

400

600
Time (ns)Figure 4.8: (Left) Waveform with laser. (Right) Diﬀerential waveform. The reproduced waveforms are superimposed with decomposed into components. The increase and the decrease in
the diﬀerential waveform was consistent each other. The reproduced diﬀerential waveform was
obtained by subtracting reproduced waveform without laser from that with laser, and decomposed
into the increase and following decrease of 1S-Ps decay. Parameters in the model are summarizedin tables in the figure.

The consistency between the increased γ-rays from 2P-Ps and the decreased γ-rays from lessremained 1S-Ps was also confirmed. In the pulse-by-pulse analysis, the ratio between increased
and decreased counts was determined by the detection eﬃciencies estimated by the Monte Carlosimulation. As shown in Figure 4.5, both of the increase and the decrease were consistently
reproduced. I L was estimated as I L = 0.74 ± 0.03(stat.) ± 0.04(sys.), which corresponded that
52 ± 2(stat.) ± 2(sys.) % of remained Ps at the timing of the laser irradiation decayed into γ-rays.
This consistency between the increase and the decrease was also confirmed by the SSPALS
analysis. Figure 4.8 (left) shows results of fitting the reproduced waveform to the measured
waveform with laser, and Figure 4.8 (right) shows the diﬀerential waveform and the corresponding
reproduced waveforms. NoPs and Γpo before the laser irradiation were also fixed by analyzing thedata without laser while Γpo after the irradiation of the laser were set to be free parameters. σL
was fixed to that from the pulse-by-pulse analysis because the response function of the detector,
which was used in the SSPALS analysis, had much wider width than σL . The waveforms
were also well reproduced by the SSPALS analysis. The reproduced diﬀerential waveform in
Figure 4.8 (right) was decomposed into increased (Sinc ) and decreased (Sdec ) components defined59

by the following equations:( ∫ t)Sinc (t) = ε L ΓL (t)NoPs exp −(Γpo (t ′) + Γs + ΓL (t ′))dt ′ ,
(4.1)
0
( ∫ t
)(
( ∫ t
))
′
′
′
′
Sdec (t) = −(ε2 Γpo (t) + ε3 Γs )NoPs exp −(Γpo (t ) + Γs )dt 1 − exp −ΓL (t )dt .
0

0

(4.2)
Sinc represents the increased intensity by decays of 2P-Ps, and Sdec represents the decreased
intensity from self decays of remained 1S-Ps. Both components are superimposed in the figure
to easily understand how each component contributed the resulted waveform. I L was estimatedas 0.72 ± 0.03(stat.) +0.01−0.02 (sys.) , which was consistent with the pulse-by-pulse analysis. In the
SSPALS analysis, the systematic uncertainty from the estimation of the timing profile of thepositrons was also evaluated. The decay model was able to describe the enhanced decay of
2P-Ps, and the both analysis methods were able to yield consistent results.

4.3 Quantitative analysis of the broadening and the decay rate
4.3.1 Estimations of the width of the broadening and the decay rate
The decay rate of the confined 2P-Ps, Γ2 , was estimated by comparing measured resonancespectra by the model. Resonance spectra were measured by irradiating laser at diﬀerent timings.
Because 1S-Ps had the time dependent mean kinetic energy through the thermalization process,it was expected that the mean kinetic energy of 2P-Ps at the excitations was able to be varied bychanging the timing of the laser irradiation (t L ). Figure 4.9 shows the resonance spectra measured
with fine steps of the wavelength, and a result of scanning t L at the center of the resonance. The
resonance spectra were obtained with 330 µJ, and the timing scan with 485 µJ pulse energy of
the UV laser at the sample. The results from the SSPALS analysis are shown here.
At every t L the similar broad line widths as wide as 1 nm in FWHM were observed asin the previous work [2], but the peak I L were not uniform. The assumed model is not able
to describe these behaviors without a modification because the line width and the peak value
correlate each other as shown in Figure 3.20. It implies that an inhomogeneous broadening takes
eﬀect in the aerogel. A Gaussian shape profile was introduced to model the broadening eﬀect,
whose possible origin is discussed later in subsection 4.4.1. Observable resonance spectra wereobtained by calculating averaged I L from the intrinsic resonance spectra and the broadening
profile. Since the intrinsic resonance spectra depend on Γ2 , Γ2 and the width of the broadening
σB were able to be determined by globally fitted to the measured data. Because the data showedthat I L decreased in time from around t L = 90 ns, it is implied that Γ2 decreased from a certain
Ps kinetic energy. Γ2 is modeled by a toy function of the energy E as
Γ2 (E) =ΓM.
1 + exp(−(E − Eth )/Eb )The four parameters are estimated by fitted to the measured data.
60

(4.3)

Intrinsic resonanceReproduced𝑡" = 20 ns

IL

Broadening profile 𝜎- = 0.39 ± 0.02 nm

IL

Measured𝑡" = 70 ns

1

1

0.5

0.5

243

0

244
Wavelength (nm)𝑡" = 310 ns

242

243

244
Wavelength (nm)

IL

242

IL

0

At the center of the resonance

1.5

1

0.15
1
0.1

0.5

0.5
0.05
242

243

0

244
Wavelength (nm)

0

100

200

300

400
tL (ns)

0

100

200

0

0.1

0
Ps

G2 (GHz)0

Figure 4.9: Resonance spectra and timing scan of I L1.5
. The reproduced curves were obtained by 15000
averaging the intrinsic resonance spectra over the broadening profile. The same width of thebroadening profile was used for all curves.
10000
1
5000
0.5
0.05

61

0.1

0.15

0

Table 4.1: Sources of uncertainties related with measurements and analysis, and their eﬀects for
estimating I L . The largest eﬀect is quoted for the source whose eﬀect significantly depended on
t L or wavelength of the laser.
SourceUncertainty of the source

Eﬀect on I L±2%Statistics
Detection eﬃciencies

2%

±2%

Estimation of the timing
profile of the positrons

Described in section 3.3.1+0%/−40% for t L = 8 ns

Deviation from thepulse-by-pulse method

Described insubsection 4.3.4−40% in maximum fort L = 310 ns and wavelengthof 244.2 nm. Typically±10%.

Table 4.2: Sources of uncertainties related with the decay model, and their eﬀects for estimating
I L . The largest eﬀect is quoted for the source whose eﬀect significantly depended on t L or
wavelength of the laser.
SourceUncertainty of the source

Eﬀect on I L

Jitter of pulse energy of the
UV laser6%±6%

Misalignment between thelaser and the positrons

1 mm

±7%

Estimation of kinetic energyof Ps

Shown in Figure 4.10 and
Figure 4.11

±12% for t L = 210 ns

Uncertainties shown by error bars in Figure 4.9 were used as inverses of the weights for the
least squares fitting. Contributions from statistical and systematic uncertainties are combined.
Sources of uncertainties and their eﬀects for estimating I L are summarized in Table 4.1 andTable 4.2. The uncertainty of kinetic energy of Ps was evaluated from the discrepancy between
the expected and measured time evolution of the pick-oﬀ decay rate shown in Figure 3.10. A
range of the uncertainty of the energy was determined to reasonably include measured pick-oﬀ
decay rates. Figure 4.10 shows the range of the uncertainty. Measured pick-oﬀ decay rates
were converted into the kinetic energy according to the RTE model. Figure 4.11 show magnified
views in diﬀerent ranges.
σB and parameters to describe Γ2 (E) in Equation 4.3 were estimated by fitted to the measured data in Figure 4.9. Fitted resonance spectra and timing dependence of the peak I L aresuperimposed in Figure 4.9, and resulted Γ2 (E) is shown in Figure 4.12. The time durationof the laser pulse in the model was set to reproduce measured σL . Γ2 was estimated to be
62

Measured (SSPALS)

3

2

1

1

0

200

0.8

400

Measured (SSPAL
Measured (Pulse-b
Graph
Graph
Graph

3

Measured (Pulse-by-pulse)

2

0

0

600
Time (ns)Range of uncertainty

0

200

0

200

0.6

1

Estimated by measured pick-off decay rates

0.4

0.5

0.2

0

200

400

600
Time (ns)Measured (Pulse-by-pulse)

Measured(SSPALS)
Measured(Pulse-by-pulse)

3

Graph
Graph
Graph

Measured (Pulse-by-pulse)

4

0.2 3

2

2

2
0.1

1

1

1

0

Ps kinetic energy (eV)-1G
G22 ((µµss-1))

Measured (SSPALS)

0

0.8

200

400

Range of uncertainty
Best estimation

0.6

Estimated by measured pick-off decay rates

0.4
0.2
0

0

600
Time (ns)Ps kinetic energy (eV)G 2 (µs-1)

Figure 44.10: Uncertainty of time evolution of Ps kinetic 4energy. The range of the uncertainty
was determined to reasonably include measured points.
Measured (SSPALS)

400

0

200
200

400 400
600 600
Time Time(ns) (ns)0

Ps kinetic energy (eV)

0

3

400

Best estimation

G2 (µs-1)

Ps kinetic energy (eV)4

G 2 (µs-1)

G 2 (µs-1)

4

0

200

0

200

Range of uncertainty

1
0.12

1

Best estimation
Estimated by measured pick-off decay rates

0.10
0.08
0.5

0.5

0.06
0.04

0

20

40

60
Time (ns)

00

200
200

400
400

600
600
Time (ns)Figure 4.11: Magnified views of the uncertainty of time evolution of Ps kinetic energy.

63

IL

1.5
0.15

0.15

Result1 of the fitting
0.1

Γ"

/
6.8 *(.+'(.) ×10 GHz

0.05
𝐸

'8 eV
5.0 *(./'(.7 ×10300

400tL (ns)G2 (GHz)

200

45
0
00
𝐸;

100
100*=.> 200 '/300
5.8
eV'8.< ×10

0.05
400tL (ns)0
G2 (GHz)

0.5

0.1

1.5
8000
6000

1
4000

0.15

0

200

300

400

8000
6000
4000

Measured
Best estimation
Uncertainty

2000
0.5
0.1

100

0 0.050.05

Measured
Best estimation
Uncertainty

2000
0

0.1
0.15
0.1
0.15 0.2
Ps kinetic energy (eV)

0.04

0.06
0.08
Ps kinetic energy (eV)Figure 4.12: Resulted Γ2 (E) and the measured points. The right figure magnifies around thepoint from which the decay rate started to decrease.

64

G2 / (Classical collision rate)

3

Best estimation
Uncertainty

2

1

0

0

0.05

0.1
0.15
0.2
Ps kinetic energy (eV)Figure 4.13: Energy dependence of the decay probability of per a collision. The classicalcollision rate was assumed by L/v where v was velocity. The resonance around 0.06 eV wasobserved. The dashed line was in an extrapolated region where data did not exist.
(6.8 + 0.8/−0.6) × 103 GHz in maximum and start to decrease from around 0.06 eV down toaround 1 THz for the thermalized Ps. The line width was broadened as wide as 0.39 ± 0.02 nm
in one sigma, which corresponded to 0.92 ± 0.05 nm in FWHM.
A decay probability per a collision in the pores can be estimated from Γ2 (E). A rate ofcollision was classically assumed to be L/v where L = 34 nm as the mean free path in the
pores, and v is velocity of Ps. Figure 4.13 shows the calculated probability against Ps kinetic
energy. The probability was in the order of unity. It can be interpreted that the decay occurredin every collision with the pore surface. The probability had the peak at around 0.06 eV. Thisimplies that a bound state was possibly formed between 2P-Ps and the surface as discussed insubsection 4.4.2.

4.3.2 Dependence of the enhanced decay on radicals induced by the UV laser
The quenching of o-Ps by radicals induced by the UV laser was observed during the measurements, but the amount of the radicals did not aﬀect the enhanced decay of 2P-Ps. As describedin section 1.1.2, the radicals were increased in time by irradiating the UV laser on the aerogels.
Figure 4.14 shows the timing spectra measured at diﬀerent accumulations of the radicals. Measurements of the resonance spectra by scanning the wavelength were performed after scanning
the timing of the laser in fine steps at the center of the resonance. The decrease of o-Ps by theaccumulations of radicals was clearly observed. NoPs decreased and Γpo increased by around
25 % in the wavelength scan compared with during the timing scan, but observed I L decreased
as shown in Figure 4.9. This decrease was able to be explained by the decrease of the pulse
energy of the UV laser between scans. Calculations including the decrease of the pulse energy
were able to globally explain the both scans shown in Figure 4.9. The radicals induced by the
UV laser had less eﬀects on the decay of 2P-Ps.
65

Counts (/10ns /bunch)1

Before laser irradiation
During timing scan

10−1

During wavelength scan

10−2
10−3
10−4
0

500

1000
Time (ns)Figure 4.14: Timing spectra measured at diﬀerent accumulations of the radicals. More radicals
were accumulated during the wavelength scan, and they quenched o-Ps to reduce NoPs andincreased Γpo by around 25 %.

4.3.3 Less pick-oﬀ decay by the energy selective decay of 2P-Ps
Decreases of the pick-oﬀ decay rate after the irradiations of the UV laser were observed because of
the larger Γ2 for more energetic Ps. The left of Figure 4.15 compares the pick-oﬀ decay rates withand without the laser irradiations, and the right shows an example of the timing spectra, which
was acquired with t L = 160 ns. The pick-oﬀ decay rates were calculated by the pulse-by-pulse
analysis. The fittings to estimate the pick-oﬀ decay rates were performed from 240 ns or later
than t L . As shown in the right of Figure 4.15, the slope of the spectrum became more flat withthe laser. This means that the less pick-oﬀ occurred after the irradiation of the laser. The pick-oﬀ
decay rate averaged over t L decreased by 28 ± 5 % from 1.06 ± 0.02 µs−1 to 0.76 ± 0.05 µs−1 .
The dependence of Γ2 on the kinetic energy is able to explain the decrease of the pick-oﬀ decayrate since more energetic Ps is more probable to decay in the 2P state to result in the less pick-oﬀ
decay for the remained 1S-Ps. Figure 4.16 shows a calculated variation of the energy distributions
by the energy selective decay of 2P-Ps with assuming Γ2 (E) in Figure 4.12. The distribution
without the laser was assumed to be Maxwell-Boltzmann distribution with 380 K to simulate databy t L = 160 ns. The mean energy was estimated to decrease by 25 % from 0.049 eV to 0.037 eV.
This deceleration can consistently explain the decrease of the pick-oﬀ decay rate, which is almost
linear function of the kinetic energy as described in Figure 1.4.

4.3.4 Consistency between the analysis methods
The consistency of the results by the two analysis methods was checked. Figure 4.17 compares
resonance spectra and timing dependence of I L obtained by both of the methods. Error barsof the points hereby represent only uncertainties summarized in Table 4.1, which are relatedwith measurements and analysis, to see deviations by analysis methods. In the pulse-by-pulse
analysis, I L were estimated by fitting the decay model to the data from 240 ns or later than t L
66

c2 / ndf

33.63 / 23
0.07067
1.057 ± 0.01692

Prob
p0

1.5
1
0.5

400

0

c / ndf
33.61 / 23
Prob
0.071
p0
0.7565 ± 0.04653
2

0

100

200

300

400
tL (ns)Counts (/10ns /bunch)

G po (µs-1)21Without laser-1

10With laser𝑡" = 160 ns

10-2
10-3
10-4
0

500

1000
Time (ns)Figure 4.15: Decreases of the pick-oﬀ decay rates by energy selective 2P-Ps decay. (Left) Pick-oﬀ
decay rates for various t L . (Right) Example of the timing spectra. The spectrum was obtainedwith t L = 160 ns. The less steep slope was observed with the laser. This is the result of theenergy selective decay of 2P-Ps.

Density (eV-1)

00

Without laserWith laser

25

Without laser
20With laser
15
10
5
0

0

0.1

0.2
0.3
Ps kinetic energy (eV)Figure 4.16: Decrease of kinetic energy by energy selective 2P-Ps decay. The decrease of thepick-oﬀ decay rate was able to be explained by the deceleration.

67

1.0

𝑡" = 20 ns

IL

SSPALS
Pulse-by-pulse
FittedIL
1.5
1𝑡" = 70 ns

0.151

0.1
0.5

0.5
0.5

0.05
0

242
100

200
243

0.5
1.5

0

300 244
400(ns)
WavelengthtL(nm)

0

242
100

10000

𝑡" = 310 ns

0.4ILG2 (GHz)

IL

0.0
0

0.3
1

200
243

300 244
400
Wavelength (nm)At the center ofthe resonance

1.5

0.15

1.0
5000

0.1

0.2
0.5

0.1
0.5
0.05
242

0.1
243

0.00
00

0.15244
Wavelength (nm)

0.1
100

2000.2 300 0.3 400 0.4
tL (ns)Ps kinetic energy(eV)Figure 4.17: Comparisons of the resonance spectra1.5and the timing dependence of I L . Bothresults agreed at later t L , and the same tendency of the dependence of Γ2 on the kinetic energy
was observed. Disagreements could be explained by inevitable systematic errors from theextrapolation in the pulse-by-pulse analysis.
1

0

10

0

0

10000

G2 (GHz)

0

0.05

5000

0.5
0.05

68

0.1

0.15

0

in order to estimate NoPs and Γpo , and then extrapolating the model function to estimate NoPs att L . Both results agreed at later t L , and the same tendency of the dependence of Γ2 on the kinetic
energy was observed. The lower I L at early t L by the pulse-by-pulse analysis could be obtainedby a systematic error from the long extrapolation. For t L before 30 ns, not all of the positrons
in the beam were arrived at the timing of the laser irradiation to result in the spurious decreaseof the estimated ratio of decayed Ps. The results after t L = 30 ns were also lower by around
10 % than the SSPALS method. This could be attributed to the decrease of Γpo by the energy
selective decay, because the eﬀect of the extrapolation would become diﬀerent. It is assumed
from Figure 3.10 that Γpo is twice as large as the thermalized value during 100 ns from theproductions of Ps. NoPs could be systematically lower by the extrapolation using Γpo ≃ 1 µs−1 ,which was typically estimated by analyzing data without laser. The eﬀect is evaluated as large as
10 % for NoPs by exp((2Γpo − Γpo ) × 100 ns) − 1 = 0.10. Because of this systematic error which
can appear at early t L in the pulse-by-pulse analysis, estimations described in subsection 4.3.1
were based on the SSPALS analysis. Deviations between the two methods were included into
the uncertainties for data at t L > 240 ns, where the extrapolation was not performed.

4.4 Discussion
It is necessary to suppress the broadening and the decay process in order to realize the proposed
eﬃcient cooling scheme. Following the observations, possible directions are discussed to elucidate mechanisms of each phenomenon. Outlook for realizing the rapid cooling by suppressing
phenomena is also discussed.

4.4.1 Broadening eﬀect
In the present measurement, the broadening as large as 1 nm was observed and independent
on the decay rate. This implies that the broadening is caused by other mechanisms than thosewhich induce the decay process. One of the promising mechanisms is that a variation of residual
electric fields in the pores caused the position dependent DC Stark shift on the 2P state energy
levels. The broad resonance spectrum is obtained because the position of Ps at the excitation
should be random in the pores. Shifts of binding energy of the 1S and 2P states are calculated
against strength of the electric field as shown in Figure 4.18. A strength of the electric field tocause the shift on the energy interval as large as 1 nm can be calculated as around 400 kV/cm.
This field value is reasonably expected by contributions from remaining dipole momentsof silanol groups (−Si(OH)) on the surface of nano particles of which the hydrophobic silica
aerogel consists. Figure 4.19 shows a schematic drawing of silica nano particles with its chemicalgroups [52]. A typical powder of hydrophobic fumed silica is known to have the remaining
silanol groups as dense as σ = 0.44 nm−2 [53]. If Ps is trapped in pores, a squared mean field
which Ps eﬀectively feels can be calculated as [52]
E2 =

πσp2
2Lϵ 3

,

(4.4)

where p = 0.050 Vnm2 is the dipole moment of −OH groups, L is a mean distance between
69

Energy (eV)Energy (eV)0.02 eV = 1 nm of 243 nm
𝑜 − Ps-6.8026-6.8028-1.69|2S⟩ + |2P. ⟩-1.70|P/ ⟩, |P1 2-6.8030-6.8032-1.71

𝑝 − Ps
0

100

200
300
400
E field (kV/cm)|2S⟩ − |2P. ⟩
0

100

200

300
400
E field (kV/cm)

𝑛=2
𝑜 − Ps𝑛=1

Figure 4.18: Calculated shifts of the binding energy of Ps under electric field. Perturbed states
are shown by legends in the figure. Suﬃxes x, y, and z show the magnetic quantum state, wherez is the direction of the electric field. The broad width can be observed under around the field of
400 kV/cm.

112

A.0 Stark Shift
OH

R

R
O

OH
Si
O

O

Si
O

O

Si O
O

Si
O O

Si O
Si
Si O
O
O
O

Si
O Si

R=Si (CH3)3
OH
Si

Si

O

O
O Si O Si O
R
Si O Si O
O Si O Si R
O
O Si O Si O Si O
O
O
Si
Si
O
O
O
O
O
Si
Si
Si O Si O Si
R
R
O
O
O
O
O
Si
Si
O Si OOH
R
R

Figure4.19:A.1:
Schematicdrawingof silica
nano particles
with its chemical groups [52]. The
FigureSchematic
diagramof SiO
2 grain. Part of the surface functionalsurfaceismainlymodifiedbytrimethyl(−Si(CH))
groupsbe hydrophobic,
but a certain
3 3 silanol togroups are substituted, while there are stillgroupsleft.
amount of silanol groups are known to remain.

groups are existing on the surface of the grain. A typical size of dipole
moment for the groups −(OH) is 1.7 70
× 10−18 [esu · cm] [63].
For the sake of the simplicity, it is assumed that the dipole moment p� isdirected outward on the surface of the grain as illustrated in Fig. A.2. Then,the electric field at the point O outside the grain is expressed as,� =E

13 (�n · p�) · �n − p�
·
4πε0
R03

The squared electric field would be,

(A.9)

100

Decay rate (µs-1)

7.040100

7.040099

7.040098

7.040097
200

0

300
400
E field (kV/cm)

100

200
300
400
E field (kV/cm)

Decay rate (µs-1)

100

0.4 ppm

Figure 4.20: Calculated shifts of the self decay rate of o-Ps under electric field. The decay rate
0.8is not measurable in the current precision.
shifts only 0.4 ppm, which

0.6
grains consisting of pores, and ϵ is a minimum distance between the grain and Ps. By substituting
L = 34 nm and ϵ = 0.4 nm, which is Bohr radius of 2P-Ps, the field can be evaluated as√
E 2 ≃ 280 kV/cm. The 0.4
field is in the order of the strength to induce the observed broad widthof the resonance spectrum.
0.2the existence of such strong field and the precise measurement ofA consistency between
the lifetime of o-Ps in silica aerogels was checked. Figure 4.20 shows a calculated shift of the
0 electric field. The decay rate shifts only 0.4 ppm, which is not
self decay rate of o-Ps under
200 measurable
300
400
0
100
200
300
400
in the current precision.
E field (kV/cm)
E field (kV/cm)
This assumption that the residual electric field broadens the resonance spectrum can beverified by performing spectroscopy for atoms confined in the silica aerogel, while material
eﬀects especially on the probe system should be clarified beforehand [54, 55]. For example,
broad Raman spectrum was observed for caﬀeine molecule confined in a mesoporous silica
material[55]. Systematic studies using well understood and simple systems will be beneficial toelucidate the eﬀects from the material.

4.4.2 Decay process
The decay of 2P-Ps was enhanced through possibly forming the bound state whose resonance
was at around 0.06 eV. While a lot of resonant annihilations of positrons with various atoms
and molecules have been reported for low energy positrons down to around 0.1 eV [56], there
are limited reports of the quenching of Ps with forming a bound state with other systems. For
example, gases such as NO2 , Br2 , and I2 are known to quench o-Ps in the 1S state with highprobability [57–59]. It was suggested that the quenching occurs through forming bound stateswith those molecules, and can be resonant if the bound states are unstable [59]. A reason by which
the quenching occurs with only those molecules is proposed to be the small bond strengths [58],71but mechanisms are still unclear to my knowledge. The enhanced decay which was observedin the present work can be the similar quenching phenomenon. Theoretical studies including
specific properties of materials will be beneficial to elucidate the quenching phenomena.
Because the enhanced decay was observed only for 2P-Ps and less aﬀected by the radicals
in the present work, some of the distinctive features of the 2P state induce the enhanced decay.
First, the binding energy in n = 2 state is small by 5.1 eV compared with the 1S state. If thework function of 2P-Ps to silica is assumed to be same with that for 1S-Ps, which is assumed
to be in from −3 eV to −1 eV, 2P-Ps is naively expected to have the positive work function topenetrate into the bulk of silica and be dissociated through the formation of the bound state. This
assumption can be checked by using other materials with diﬀerent work functions. For example,
tungsten is an interesting target material because it has the work function around −5 eV [60]for 1S-Ps, which is close to the diﬀerence of the binding energy between the 2P state. A new
sample structure to be collided by 2P-Ps is necessary to be developed. Second, the large electricsusceptibility of the P state could enhance interactions with the material in which the residual
electric field is expected to exist. In this case, the 2S state which can be excited by two photon
absorptions of 486 nm laser will have less decay rate. It is still challenging to induce the two
photon absorptions inside the material because a high power and the good coherence are required:
the Ps converter must be transparent enough to be put in an optical resonator which accumulates
the laser power, or the more powerful laser by around 10 times than the adopted one in the present
work is required.

4.4.3 Outlook for the rapid cooling of Ps
One of the straightforward directions to realize the rapid cooling is to modify the surface structureof pores such that abnormal phenomena are suppressed. For example, the broadening will beeased by removing dielectric groups or covering pores’ surface by a metal layers so that theresidual electric field in the pores will be quenched. Furthermore, covering of the surface byappropriate materials could alter the interaction between the surface and 2P-Ps into a repulsive
one to prevent 2P-Ps from being dissociated under the string influence from the material. It is
important to systematically test eﬀects by the modifications using various type of materials.
Another interesting direction is to adopt another type of a cavity such as a bubble of liquid
helium. 1S-Ps is known to have a relatively long life time around 100 ns in liquid helium withforming a bubble [61, 62]. It was proposed that liquid helium can be a good medium of thecavity to realizing Ps-BEC [63] thanks to an expected rapid thermalization process under frequentinteractions through the surface of the bubble. It is still challenging to combine liquid helium
with a bunched positrons, which usually requires to be in a high vacuum system, but it will bebeneficial to conduct spectroscopic measurements of Ps in the bubble, and compare the resultswith theoretical predictions in order to establish methods to measure phase space density of Ps
as performed in this work.

72

Chapter 5

Conclusion
Details of the decay process of Ps in the 2P state were quantitatively studied to develop thePs confining cavity for eﬃcient cooling. The silica aerogel was used as the test sample which
had the new feature that 1S-Ps was not strongly aﬀected in it. By analyzing the data with therealistic model, the decay rate of 2P-Ps (Γ2 ) was measured as large as 7 THz in maximum, andthe corresponding probability to decay per a collision was calculated as in the order of unity. The
enhanced decay which was observed only for 2P-Ps favors that some of the distinctive features ofthe 2P state, such as the small binding energy or the high electric susceptibility, are origins of the
decay process. The resonance of the decay which were observed at around 0.06 eV for Ps kinetic
energy suggests that the decay proceeds through forming the bound state with the material. Theline width of Ps Lyman-α transition was as broad as 1 nm in FWHM irrelevant with Γ2 . Thisobservation suggests that the broadening was from not only the natural line width of the decay
but also an inhomogeneous broadening, which is possibly caused by the residual electric field in
the pores.

73

Acknowledgements
First, I would like to express my gratitude to my supervisor Prof. Shoji Asai (UTokyo) forsuggesting this work and his continuous encouragement and supports. His positive attitude
always helped me a lot to tackle this challenging and exciting work.
I also wish to express my great appreciation to Dr. Akira Ishida (UTokyo) for his indispensable
contributions. This work became realistic through his deep understanding about the whole
relevant topics, and was also further driven by his much eﬀorts in every essential but timeconsuming task, including getting scientific grants without which the most part of this work
could not be carried out.
My special thanks go to Dr. Toshio Namba (UTokyo) for his kind and appropriate guidance.
His suggestions and advice were always eﬀective and useful to solve any problems in the bestway.
Sincere gratitude is expressed to Mr. Kyohei Yamada, Mr. Yohei Tajima, Dr. Eunmi Chae,
Prof. Kosuke Yoshioka, and President Makoto Kuwata-Gonokami (UTokyo) for their excellent
contributions in operating the laser systems. A specialized laser system for Doppler cooling was
also developed by them. I also thank to Mr. Tomoyuki Murayoshi (ex-UTokyo) and Mr. Xing
Fan (Harvard University) for their important works in the early stage of the development.
I gratefully thank to Prof. Satoshi Uetake and Prof. Koji Yoshimura (Okayama University)
for kindly providing the OPO laser and the wavemeter.
My deep appreciation is expressed to collaborators at AIST. Dr. Kenji Ito and Dr. Kazuhiro
Kumagai contributed in fabrications and evaluations of the Ps converter with their outstanding
skills. Ms. Kaori Hashidate (also belongs to UTokyo), Dr. Koji Michishio, Dr. Brian E.
O’Rourke, Dr. Nagayasu Oshima, and Dr. Ryoichi Suzuki accomplished the required focusingof the positron beam and measurements using their beam line.
I sincerely appreciate Dr. Izumi Mochizuki, Prof. Toshio Hyodo (KEK), and Prof. Yasuyoshi
Nagai (KEK and Tohoku University) for their running of KEK-SPF. The high quality of thepositron beam was provided thanks to their great works. My great appreciation is expressed to
Dr. Ken Wada (QST) for his useful advice to perform experiment in KEK-SPF and to control
the positron beam.
I also express my sincere gratitude to Dr. Kengo Shibuya and Prof. Haruo Saito (UTokyo)
for the useful discussion of the possible mechanisms to induce abnormal behaviors of 2P-Ps.
It is my pleasure to thank collaborators for realizing Ps-BEC. Prof. Shigeru Fujino (Kyushu
University) and Dr. Kentaro Kawai (Osaka University) manufactured well-controlled silica
cavity. Dr. Takeshi Kai simulated dynamics of extremely dense positrons.
75

I would like to thank all staﬀs and colleagues of Dept. of Physics and ICEPP at UTokyo for
their sincere supports.
Finally, I thank my family for supporting me every moment.

76

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