Hatano Y., Katsumura Y., Mozumder A. (Eds.) Charged Particle and Photon Interactions with Matter - Recent Advances, Applications, and Interfaces

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200 Charged Particle and Photon Interactions with Matter

1 ms in order to avoid any interaction of the magnetic eld produced by the DC current with the

resonantly ionized ions (muons). The target chamber is evacuated down to ultrahigh vacuum level

of 2 × 10

−7

Pa at 2300 K. The W target is cleaned via surface treatment in 3.0 × 10

−5

Pa of oxygen

at 1800K for about 10h, and then heated up to 2000 K for the experiments. Figure 8.21 (bottom)

shows a layout of “slow-ion optics” consisting of an immersion lens (SOA), a magnetic bend for

mass separation, an electrostatic mirror, and ve sets of electrostatic quadrupoles.

1s Kr

212.55 nm

122 nm

820 nm

Muonium (Mu)

Slow µ

–

355 nm

122 nm

SOA lens

Kr (Ar) cell

NO cell

Surface

beam

VUV mirror

MCP

Electrostatic

Mirror

Bending

magnet

Hot-W

Electrostatic

quadrupole

Muon spin

212.55 nm

820 nm

212.55 nm

820 nm

122 nm

355 nm

Figure 8.21 The top gure is a resonant ionization scheme via the {1S-2P-unbound} transition for the

Muonium (Mu) and the scheme for the Lyman-α generation via the four-wave frequency mixing method

using two 212.55nm (ω

) photons for the two-photon resonant excitation of the 4P55P [1/2,0] state in krypton,

subtracted by a photon with a tunable difference wavelength (Nagamine et al., 1995; Bakule et al., 2008). The

bottom gure is a layout of “slow-ion optics” consisting of an immersion lens (SOA), a magnetic bend for mass

separation,

an electrostatic mirror, and ve sets of electrostatic quadrupoles.

Muon Interactions with Matter 201

8.6.2.2 unique Features of the pulsed ultraslow μ

beam

8.6.2.2.1

Pulse Width

One of the most important features of the ultraslow μ

beam generated by the resonant laser ioniza-

tion of Mu is its short pulse width. Regardless of the temporal prole of the surface muon pulse—

with its double bunch structure consisting of ∼100ns (full width at half maximum [FWHM]) pulses

separated by 320ns at RIKEN-RAL—the pulse duration of the ultraslow muon beam is determined

only by the duration of the laser pulse and by the transport properties of the low energy ion transport

beamline. Consequently, at RIKEN-RAL the duration of the ultraslow μ

pulse in the time-of-ight

spectrum at the end of the transport beamline is just 7.5ns (FWHM). In principle, the pulse dura-

tion can be reduced further to ∼1ns by using a laser with shorter pulse duration and optimizing the

beamline transport. There is another advantage of this pulsed method—the capability to externally

trigger when the muonium is ionized, that is, to trigger the ultraslow μ

pulse width. This is possible

because of the relatively low velocity of the thermal Mu cloud. The Mu atoms that are emitted from

the W target foil stay near the surface of the foil, with their concentration not signicantly changing

over a timescale of ∼500ns. Within this timescale, one can then choose when to trigger the laser

pulse to generate the low energy muons. Such a feature is extremely useful for pump-probe type

experiments where synchronization of the muon implantation with some other sample excitation

(e.g.,

by another laser, rf pulse, etc.) is required.

8.6.2.2.2

Beam Size and Energy Resolution

Since Mu atoms evaporate from the hot W (2000K) at thermal energies, the initial kinetic energy

of the ultraslow μ

generated by the laser resonant ionization is only 0.2eV. Therefore, the beam

emittance of the ultraslow μ

beam accelerated by SOA lens to 9 keV is so small that the beamcan

be focused onto a tiny spot on the sample. Compared to the size of the incident surface muon beam

of 40mm (FWHM), the resulting ultraslow μ

beam could be focused to a spot of just 3.3mm

(FWHM, horizontally) by 4.1mm (FWHM, vertically) presently at RIKEN-RAL. In principle, the

beam size is not limited by the beam emittance but by the transport characteristics of the beamline

and by better optimization of the beamline, spots as small as 1mm (FWHM) can be potentially

obtained, perhaps at a cost of reducing the transport efciency. According to the evaluation by

Bakule et al. (2008, 2009a,b), energy resolution of the low energy muons is only σ

= 14 eV (33eV at

FWHM) at RIKEN-RAL, which is in contrast with σ

= 400 eV (950eV FWHM) at PSI because of

energy spread caused by the thin trigger counter at PSI. Having such an essentially monoenergetic

beam

is very important for near-surface studies on depth scales of 0–10

nm.

8.6.2.2.3

Polarization of the Ultraslow Muons by the Laser Resonant Ionization Method

Although the surface muons are 100% polarized initially, the polarization of the singlet Mu, in

which the muon and electron spins are parallel, is depolarized due to the hyperne interaction of

the paired electron. Therefore, the ultraslow μ

produced by the laser resonant ionization method is

only 50% spin polarized only by the contribution of the triplet Mu (Miyake et al., 1997). Possibly,

re-polarization of the singlet Mu by the external strong longitudinal eld might be performed with

future

developments.

8.6.2.2.4

Yield of Ultraslow Muons by the Laser Resonant Ionization Method

At the RIKEN-RAL muon facility, 20 ultraslow μ

−1

(Bakule et al., 2008) can be extracted out of

1.2 × 10

−1

surface muons from the sample. At the J-PARC MUSE super omega muon channel,

4× 10

surface muons s

−1

can be extracted from a large acceptance of 400msr. From the viewpoint

of the intensity of the surface muon, we can gain a factor of 300. Taking into account the repetition

rate of the pulsed laser system and the muon beam, we can gain a factor of two, since at J-PARC,

both the laser and muon beams can be synchronized to 25Hz, whereas at the RIKEN-RAL

202 Charged Particle and Photon Interactions with Matter

facility, the muon beam (50Hz) is synchronized to every second laser pulse. Therefore, we can

expect 1.3×10

−1

of the ultraslow μ

−1

without any additional laser development at J-PARC

(Miyake etal., 2009).

Although more than 71 μJ cm

−2

of the Lyman-α light is needed in order to saturate the tran-

sition of Mu from the 1S state to the 2P state, we are, at present, producing <1 μJ cm

−2

of the

Lyman-α light through the resonant four-wave frequency mixing (ω

VUV

= 2 ω

− ω

; 212.55nm

(ω

) 820nm (ω

)). As a possible promising method to obtain a more intense Lyman-α laser source,

we are planning to adopt the tripling of 366nm photons (non-resonant tripling: ω

VUV

=3 ω

366

) with

pico second pulse width to match the Doppler broadening of the Mu at 2000 K, expecting more

than 100 μJ cm

−2

of the Lyman-α light. With sufcient laser development, we expect about 100

times increase in gain. Finally, we expect a maximum rate of 1.3 × 10

−1

ultraslow μ

−1

(Miyake

et al., 2009).

Scientists at PSI are developing a slow muon source by adopting a cryogenic moderator and

have started various kinds of surface/interface science programs, for example, those by Jackson

et al. (2000), Khasanov et al. (2004), Morenzoni et al. (2008), Senba et al. (2006), and Suter etal.

(2004). Although the J-PARC project is lagging behind that of PSI due to more time required

for the construction of the super omega channel, more intense ultraslow μ

with a smaller beam

size, a shorter temporal width, and lower background is expected at J-PARC. Table 8.2 shows a

comparison of the slow muon beam between the PSI cryogenic method and the J-PARC resonant

ionization of Mu.

8.6.2.2.5

Aspects of the Charged Particle Interactions on the Ultraslow μ

Generation

The mechanism of the emission of the thermal Mu may include important features of the charged

particle interactions with matter. Laser resonant ionization is one of the most powerful methods

to study the mechanism for the emission of thermal neutral atoms originating from high-energy

nuclear reactions, owing to the capability of isotope/particle selection as well as a high efciency.

This idea has been used as a chemically selected laser-ionized ion source for unstable heavy

nuclei at CERN-ISOLDE (On-line Isotope Mass Separator at CERN) (Mishin et al., 1993). By

only changing the difference wavelength (ω

) in the present four-wave frequency mixing method

without changing any other experimental condition, the Lyman-α wavelength can be easily tuned

for any hydrogen isotopes. A very important capability of the laser resonant ionization technique

is that it enables us to very efciently detect and distinguish even hydrogen isotopes existing at

the same location by adjusting the individual Lyman-α wavelength.

table 8.2

Comparison

of Features of slow m

uon

eam

btained

by the Cryogenic

oderator

sing

olid

or a

and l

aser

esonant

onization

MUON Facility

ultraslow μ

generation by laser

esonant ionization of mu

low-energy μ

generation by

Cryogenic

moderator of ar

KEK,

RIKEN-RAL and J-PARC PSI

Energy 0.1–30

keV 0.5–30keV

Monochromacity 14

eV (RIKEN-RAL), (started with 0.2

eV) 400eV

Beam

size

1–4

mm ϕ

10–15

Time

resolution

sub

ns ∼ ns ∼10

Polarization 50% 92%

Beam

intensity 20

−1

(RIKEN-RAL), 10

4–6

−1

(J-PARC) 10

3–4

−1

Synchronization Possible Not possible

Muon Interactions with Matter 203

Figure 8.22 (top) summarizes the resonance spectra for all hydrogen isotopes (Mu, H, D,

and T). The observed resonance peaks agree with the calculated values. The width of the Mu

resonance is consistent with the FWHM expected due to Doppler broadening and a Mu tempera-

ture of 2000 K. In the case of H, the resonance curve was taken as a cold run from the residual

hydrogen in the UHV chamber. Figure 8.22 (bottom) shows the temperature dependence of the

total yield of Mu andT. The Mu evaporation was negligible at the temperature below 1200 K,

started to increase above 1200 K, and increased monotonically with temperature and leveled off

at ∼2000 K. The T evaporation was also negligible below 1500 K and increased with temperature

2500

2000

1500

121.50 121.55 121.60 122.05

Lyman-α wavelength (nm)

; Muonium generated by 500 MeV p

; Hydrogen (residual in UHV)

; Deuterium generated by 500 MeV p

; Tritium generated by 500 MeV p

122.10 122.15

1000

500

Ionization yield (a.u.)

0.3

0.2

0.1

0.0

T; E

= 1.89 (1) eV

(a)

(b)

Mu; E

= 1.72 (5) eV

500 1000 1500

Temperature (K)

T yield (a.u.) Mu yield (a.u.)

2000 2500

Figure 8.22 The top gure is a resonance curve of the laser resonantly ionized Mu, H, D, and T, where

Mu, D, and T were generated by nuclear reactions of 500 MeV protons and the H atoms were extracted from

residual hydrogen in the UHV chamber. A bottom gure shows the temperature dependence of the total yield

Mu and T. The solid lines are ts to the temperature dependence Equation 8.24.

204 Charged Particle and Photon Interactions with Matter

above 1500 K. The solid lines in Figure 8.22 (bottom) are ts to the temperature dependence

Equation 8.24 shown below:

y T

c T e

( ) ,=

−

(8.24)

where E

is the activation energy of hydrogen-like atom in eV. A least square t of Equation 8.24

to the data gives E

= 1.72 (5) eV and E

= 1.89 (1) eV. The binding energy of surface H atom rela-

tive to the free Hydrogen in vacuum is 2.95 (2), 3.03 (3), and 2.94 (2) eV for W(100), W(110), and

W(111) (Tamm and Schmidt, 1971), respectively. Therefore, H atoms are bound to the W surface by

∼2.97 (2) eV averaged over W(100), W(110), and W(111). In contrast, since the molecular H

binding

energy E(H

) and the solution enthalpy of H in W is given to be 2.24eV (Herzberg and Monls,

1960) and −0.68eV (McClellan and Oats, 1973), respectively, the work function of hydrogen to the

solid

is estimated to be ∼1.56

(Mills et al., 1986).

Thermionic

emission is a process that competes with trapping at the surface and with a loss due

to μ

-decay for Mu and trapping at impurities. However, our experimental evidences indicate that

both the lightest and heaviest hydrogen isotopes, Mu and T, are thermionically emitted from the

bulk not likely to be trapped at any surface. The difference of ∼0.2 eV between E

and E

can be

explained by a contribution of the ZPE to the Mu work function (Miyake etal.,1999).

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209

Electron Localization

and

Trapping in

Hydrocarbon

Liquids

Gordon L. Hug

University of Notre Dame

Notre

Dame, Indiana

and

Adam

Mickiewicz University

Poznan, Poland

Asokendu Mozumder

University of Notre Dame

Notre

Dame, Indiana

Contents

9.1 Introduction .......................................................................................................................... 210

9.2 Localization.......................................................................................................................... 210

9.2.1 Localization

and Trapping........................................................................................ 210

9.2.2

Disorder:

The Anderson Model................................................................................ 211

9.2.3

Relevance

to Hydrocarbon Liquids .......................................................................... 212

9.2.4

Basic Derivations...................................................................................................... 213

9.2.5 Mobility

Edge: Scaling Theory Results ................................................................... 216

9.2.6

Application

to Liquid Hydrocarbons ........................................................................ 219

9.3

Trapping................................................................................................................................223

9.3.1 General

Features.......................................................................................................223

9.3.2

Models of Preexisting Traps.....................................................................................224

9.3.3 Structure

of Traps in Nonpolar Media......................................................................225

9.3.4

Timescale

of Trapping and Trap Size.......................................................................226

9.4

Mobility ................................................................................................................................226

9.4.1 Basic

Considerations.................................................................................................226

9.4.2

Empirical Relationships............................................................................................ 227

9.4.3 Theory........................................................................................................................229

9.4.3.1 Hopping

Models.........................................................................................229

9.4.3.2

Two-State

Models ......................................................................................230

9.5

Concluding

Remarks ............................................................................................................ 231

Acknowledgments..........................................................................................................................232

References...................................................................................................................................... 232