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

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190 Charged Particle and Photon Interactions with Matter

The other question that was addressed by these works was as follows: How would the tempera-

ture or pressure dependence of the self-dissociation of water (Figure 8.16) affect the radiolysis of

water

and radical chemistry?

For

most of these works, The TF-μSR technique has been employed. It was expected that the

hyperne coupling constant of muonium would give information regarding interactions of Mu with

the water molecules comprising the solvent cage around it. This expectation was realized and it was

found that the cage around muonium changes signicantly under subcritical and supercritical condi-

tions,

as shown by Ghandi et al. (2000).

The

HFCs were determined from the splitting of the muonium precession frequencies in an

intermediate eld, typically 200 G. The results for the HFCs were consistent with a break in the cage

structure at higher temperatures. This could be evidence for smaller cooperative interactions among

water molecules at higher temperatures. Indeed, the hyperne coupling constant of Mu was found

correlate with the bimolecular collision frequency.

Very

close to the critical point, the hyperne coupling constant of Mu was found to deviate from

a smooth model. This was attributed to a local density enhancement. It is important because the

0.0E+00

4.0E–04

8.0E–04

1.2E–03

1.6E–03

2.0E–03

0 100 200 300 400

Temperature (°C)

Viscosity (Pa s)

0.E+00

5.E–05

1.E–04

η (Pa s)

0.E+00

5.E–05

1.E–04

400 bar

300 bar

224 bar

Temperature (°C)

450400350300

Figure 8.15 Viscosity as a function of temperature at pressures above critical point.

250 bar

300 bar

Temperature (°C)

200 300 4000 100

Normal

aqueous

reactions

400 bar

Free radical

reactions

OHOH

Figure 8.16 The dissociation constant of water as a function of temperature at different pressures and the

typical

chemistry involved in each region.

Muon Interactions with Matter 191

hydrophobic nature of Mu under standard conditions makes it similar to nonpolar organic com-

pounds

and gases used in SCW oxidation reactors.

Theses

studies have led to the work on muoniated organic free radicals and muonium kinetics in

subcritical and SCW. For example, the μSR technique has been used to study radical formation in

aqueous solutions of acetone by Ghandi et al. (2003), Ghandi (2002). These investigations proved

that the μSR technique is uniquely able to provide mechanistic information for radical reactions in

SCW. The study of muon hyperne coupling constants in muoniated radicals in SCFs by Cormier

et al. (2009), Ghandi et al. (2003), and Percival et al. (2000, 2003) has also demonstrated the unique

ability of μSR to probe temperature, pressure, and solvent dependence of hyperne coupling con-

stants under extreme conditions. For the rst time, radical addition to the enol form of acetone

has been observed. The studies in supercritical CO

by Cormier et al. (2009) also demonstrated

the value of μSR to test theories of the temperature and density dependence of hyperne coupling

constants.

The investigations with acetone by Ghandi et al. (2003) and Ghandi (2002) could be considered

as simple examples of multi-step synthesis. These examples show that it is possible to tune the

properties of water so as to produce the precursors of a radical under one thermodynamic condition

and then tune to another thermodynamic condition, which gives the highest concentration of the

radical. Fullcharacterization of free radicals in SCFs was carried out by a combination of TF-μSR

and ALC-μSR by Cormier et al. (2009) and Percival et al. (2003, 2005). This gave the ability to

provide both the magnitude and sign of the coupling constants in dilute solutions (Percival et al.,

2003; Cormier et al., 2009) and as well provided a tool to explore the effect of concentration of radi-

cal

precursor under extreme conditions of subcritical uids and SCFs.

The

studies on kinetics in subcritical and SCW by Ghandi and Percival (2003), Ghandi et al.

(2002) and Ghandi (2002), and Percival et al. (2007) could be considered as an extension of the work

of Troe and his coworkers (see Schwarzer et al., 1998). Troe and his group have extensively studied

kinetics over a wide range of conditions from the liquid phase to the gas phase in simple molecular

uids

such as nitrogen and simple hydrocarbons.

Although

qualitatively the ndings of the works in Ghandi and Percival (2003), Ghandi et al.

(2002) and Ghandi (2002), were similar to the ndings of Troe and his group, it was found that Troe’s

model could not describe our results in subcritical and SCW. It was also found that the analysis of the

temperature dependence by means of the model widely used by Buxton et al. (1988) and his cowork-

ers for the reactions of H and other radiolysis transient species does not give sensible parameters. The

experimental strategy was to study kinetics to separate the effect of transport (viscosity) from other

solvent effects. To do this they studied a reaction without a signicant activation barrier. This was the

spin exchange between Mu and Ni

(Ghandi et al., 2002). Spin exchange reactions are expected to

be diffusion controlled, but at elevated temperatures the rate constants were found to have values far

below those predicted by Stokes–Einstein–Smoluchowski theory. For spin exchange, the nding that

the rate constants go thorough a maximum under subcritical conditions was attributed to a decrease

of the encounter time under those conditions. Such a decrease resulted in a transition from the strong

exchange to the weak exchange limit. This should be a general phenomenon for all spin exchange

reactions in subcritical and SCW. The study of temperature dependence of near-diffusion-controlled

reactions also gave similar results; the rate constants pass through a maximum under near-critical con-

ditions and then fall with an increase in temperature. In the fall-off region, the rate constant increases

with pressure. It was found that the efciency of the reactions depends on the number of collisions

over the duration of the encounter (Ghandi et al., 2002).

If this effect is general (since the temperature dependence of the encounter time depends mainly

on solvent properties), similar observations should be expected for different types of reactions.

Therefore, further reactions were studied based on three criteria: experiments to test the stability

of reactants under a wide range of temperatures and pressures, theoretical calculations, and impor-

tance of the reaction for industry. The reactions between Mu and HCOO

−

, and Mu and OH

−

were

studied because they were expected to show strong solvent dependence (Ghandi 2002). Also,the

192 Charged Particle and Photon Interactions with Matter

reactions between Mu and benzene in Ghandi (2002) and Mu and methanol in Ghandi et al. (2003)

were chosen since they were expected to have small solvent effects, and therefore the effect of

multiple collisions was expected to be more important. There are some general trends among all

these reactions: it is clear from Figures 8.17 and 8.18 that pressure dependence is more signi-

cant at temperatures close to the critical point; there is positive pressure dependence under near-

critical conditions. For all reactions, the rate constants pass through a maximum in temperature

under near-critical conditions; both temperature dependence and pressure dependence under near-

critical conditions were consistent with the cage effect suggested for near-diffusion-controlled

200 250 300 350 400 450

Pressure (bar)

(10

–1

)

Figure 8.17 Rate constants for the reaction of Mu with formate in water at various temperatures:

290°C(□), 378°C (○), and 385°C (△). The lines through the data only serve to guide the eyes. (From Ghandi,

K., Muonium kinetics in sub- and supercritical water, PhD thesis, Simon Fraser University, Burnaby, British

Columbia,

2002.)

0.0

1.0

2.0

150 200 250 300 350 400

Pressure (bar)

(10

–1

)

Figure 8.18 Rate constants for the reaction of Mu with hydroxide in water at various temperatures:

205°C(◆), 250°C (□), 305°C (△), 362°C (•), and 390°C (○). The lines through the data only serve to guide

the eyes. (From Ghandi, K., Muonium kinetics in sub- and supercritical water, PhD thesis, Simon Fraser

University,

Burnaby, British Columbia, 2002.)

Muon Interactions with Matter 193

reactions (Ghandi et al., 2002). At lower temperatures the solute–solvent effects were found to be

more important. In particular, in studies on reactions between Mu and OH

−

and HCOO

−

it was

found that the variation of the dielectric constant of water with temperature plays an important

role in the subcritical region (Ghandi 2002). Although both reactions between Mu and OH

−

and

HCOO

−

showed the evidence of the cage effect under near-critical conditions, the reaction of

formate showed a positive deviation from the Arrhenius extrapolation while the reaction with OH

−

showed a negative deviation.

The study of kinetics of the Mu reaction with formate can be considered as an extension of the

work of Lossack et al. (2001) to supercritical conditions. Lossack showed that in the reaction between

H and formate in water, the dipole moment of the transition state is signicantly smaller than the

dipole moment of the reactants in Lossack et al. (2001). This causes signicant destabilization of the

transition state compared to the reactants. Positive deviation from the Arrhenius temperature depen-

dence for the reaction of Mu and formate is consistent with this solvent effect under hydrothermal

conditions. At higher temperatures, the dielectric constant of water drops (Figure8.12), and there-

fore its effect on the reaction path becomes smaller. This leads to larger rate constants compared to

the predictions from Arrhenius temperature dependence with activation energy calculated from the

data

under room conditions by Ghandi (2002).

The

ab initio calculations at the density functional theory level UB3LYP with a Gaussian

6-31+G(d,p) basis set for the reaction of

Mu OH MuOH MuOH (e )

+ ⇔ ⇔ +

− − −

in the presence of

three water molecules (keeping this distance between O on OH

−

and Mu xed and optimizing other

variables at each step) (Figure 8.19) suggest the dipole moment increases along the reaction path.

The larger dipole moment of the transition state compared to the reactants suggests a negative devia-

tion from predictions based on the Arrhenius model. The result of these calculations suggests that

water molecules are involved in the transition state explicitly and they are part of the reaction coor-

dinate. In addition, the effect of the dielectric constant and the cage effect are in the same direction.

The above studies led to development of a new model consistent with the temperature and pres-

sure dependence of rate coefcients over a broad range of conditions in water. The results are useful

for

modeling radiolysis of water in pressurized water nuclear reactors.

Another

new development in the eld of muonium kinetics and reaction dynamics in liquids has

been the extension of muonium kinetics to the realm of excited-state reaction dynamics by Ghandi

al. (2007).

0.0

0.8

1.6

2.4

3.2

4.0

1 1.5 2 2.5 3

HO–H distance (Å)

Dipole moment (Debye)

–50

–25

Energy/kJ mol

–1

Figure 8.19 The solid curve is the energy of the reaction complex relative to the energy of separated

reactants (OH

−

and H), and the dotted curve is the dipole moment of the reaction complex, as a function of

HO–H

distance.

194 Charged Particle and Photon Interactions with Matter

In this work, laser-muon-spin spectroscopy in liquids has been developed, which is a technique

to study the excited-state chemical dynamics of transient species. The work has more applications

than reaction dynamics but on the reaction dynamics front, as a proof of concept reaction kinetics of

muonium and Rose Bengal in the ground and excited electronic state (triplet state) has been studied.

This work also opens the way to study chemistry of excited-state muoniated free radicals. This spec-

troscopic technique has made new directions possible both for Mu chemists and the reaction dynam-

ics community by studying kinetic isotope effects of reactions of Mu with laser pumped molecules.

8.5.3 StudieS in the gaS phaSe

The most recent and important developments in the studies of reactions of Mu and muoniated free

radicals in gas phase are as follows: (1) The time-delayed RF-μSR studies of Mu reactions with

by Johnson et al. (2005). (2) The preliminary studies of a new class of chemical bonds (ro-

vibrational bonds), where the combination of vibrational and rotational motion of nuclei would lead

to transformation of a saddle point on the electronic potential energy surface (PES) to a stable spe-

cies in the work of Ghandi et al. (2006). This was in the context of a muoniated free radical formed

from reaction of Mu with Br

. (3) Studies of direct abstraction reactions and kinetic isotope effects

(KIEs) in comparison with the H-atom analogue and with “heavy muonium,” Heμ (Arseneau et al.,

2009). Heμ is the muonic atom, α

−

, where the electron is in a 1s orbital, similar to its position in

the ordinary H atom (orMu). In the “heavy muonium,” the negative muon is in the small 1s orbital,

400 times closer to α. The atom can be treated as a heavy isotope of H, with a mass 4.116amu, that

is, 37 times Mu mass! In heavy muonium, (α

−

)

acts as the nucleus. (α

−

)

is formed by the

negative muon capture onto He, with the ejection of two electrons by the Auger process. To form

the neutral Heμ, charge exchange with an easily ionized reactant, such as Xe or NH

, is required;

therefore, studies of chemical reactions of “heavy muonium” are usually performed in the presence

of one of these species. Studies of this nature demonstrate most clearly the unique sensitivity of the

muon-based-atoms to quantum mass effects in reaction dynamics, in particular to zero-point energy

(ZPE) shifts at the transition state, exemplied by late-barrier reactions with H

. (4) The studies of

Mu reactions with vibrational excited H

in the work of Bakule et al. (2009a,b) that is an extension of

the work of Ghandi et al. (2007), that is, chemical dynamics of Mu reaction with excited-state mol-

ecules in the liquid phase to the gas phase. Although the laser effect was not signicantly above the

noise level in this work, it can be an exciting development since along with the work by Ghandi et al.

(2007), they generated a new class of experimental techniques for studies of reaction dynamics.

In addition to the above-mentioned novel works in the gas phase, there have been several theo-

retical and conventional experimental studies over the last 10 years on different systems, mostly to

investigate the KIEs. These works demonstrate the unique sensitivity of the Mu atom to quantum

mass effects in reaction dynamics, to both ZPE shifts at the transition state, exemplied by late-

barrier reactions such as the Heμ + H

reaction described above (Arseneau etal., 2009), Mu + CH

(Pu and Truhlar, 2002) (KIEs k

<< 1), and quantum tunneling exemplied by “early-barrier”

reactions like Mu + Br

(Ghandi et al., 2006) (KIEs k

>> 1) at lowest temperatures and con-

comitantly

with much smaller activation energies for Mu reactions.

There

have been studies of Mu addition reactions, both in the high-pressure limit exemplied by

the Mu + C

(Villa et al., 1999) reaction where the high-pressure limit is easily realized at mod-

erator pressures ∼1 bar, and in the low pressure (termolecular) regime where much higher pressures

(>1000 bar) are required for stabilization, in the case of small molecules with only a few degrees of

freedom, such as Mu + NO (Pan et al., 2000), Mu + O

(Himmer and Roduner, 2000), and Mu + CO

(Pan et al., 2006) reactions, in which the experimental data have been compared with the predic-

tions of unimolecular (Troe) theory. In these indirect reactions, rates for addition and stabilization

are in competition with those for unimolecular dissociation, with the overall (effective) rate constant

then exhibiting different pressure limits. Such studies are important model systems for theoretical

studies (Harding et al., 2000; Marques and Varandas, 2001).

Muon Interactions with Matter 195

In general, the experimental results of Mu reactivity in these studies continue to present challenges

to reaction theory. Therefore, an interface between experimental and theoretical data on Mu is very

useful to rene reaction dynamics theories. In the realm of collision dynamics, atomic and molecular

beam studies produced under single-collision conditions at epithermal (∼1eV) energies, with their

ability to probe ro-vibrational cross sections at the state-to-state level (Althorpe et al., 2002), play an

ever increasingly important role in assessing the interface between experiment and reaction theory.

However, at these kinds of impact energies, well above threshold, the general features of reactive col-

lision processes are often well described by classical (or quasi-classical) dynamics, so that the study

of chemical kinetics and bulk thermal rate constants, which are generally much more sensitive to

quantum mass effects in probing the details of the PES at the barrier, continue to be important. This is

truer in the case of sensitive isotopic mass probes that now extend from Mu to Heμ, a ratio of 1/37, and

hence the above-mentioned studies are unique probes of quantum mass effects in chemical reactivity.

8.6 modern slow muon beam produCtion teChniQues

The conventional muon beams are obtained from proton accelerators with proton energies higher

than 400MeV. According to the momentum of the generated muon beam, these beams are referred

to as “decay muon” or “surface muon” beams. The decay muons are obtained through the in-ight

decay of π

/π

−

, conned by a strong longitudinal eld of several tesla from a superconducting sole-

noid magnet. Muons obtained this way have high momentum, between 40 to several hundreds of

MeV

−1

. Not only positive but also negative muon beams are available (Nagamine, 1981).

The surface muons are obtained from the decay of positive pions (π

) stopped near the surface

of the pion production target in the proton beam line (Pifer et al., 1976). Compared to the decay

muons that have high momentum due to the in-ight decay of pions, the surface muons obtained

from the decay of π

at rest have a low and unique kinetic energy of 4.1MeV (corresponding to a

momentum of 29.8MeV c

−1

). Since the negative pions (π

−

) are easily captured by the nucleus, only

positive surface muon beams are available. The spin-polarized surface muons are widely used as

magnetic microprobes in materials (Schenck, 1985). The surface muon beam has a lower energy

compared to the decay muon beam, and when injected into a bulk sample, they have, therefore, an

implantation depth of just 0.1–1mm. Despite the name surface muons, it is typically used as a probe

to bulk phenomena rather than surface phenomena.

Lately, the study of surface/subsurface nanomaterials and multilayered thin lms is becoming

increasingly important. However, for that purpose, we must have muon beams that have sufciently

low energy to stop on or near the surface of the sample. To perform such studies, so called slow (low

energy) muons are required with energy that is of the order of several eV to a few tens of keV, far

lower than the energies available from the conventional muon beams. In this section we introduce

the

novel techniques to generate such slow muon beams.

8.6.1 the generation of low energy μ

through the cryogenic Moderation Method

The generation of low energy μ

through the cryogenic moderation method using van der Waals

solids,

such as solid Ar or N

, has been developed in the following four stages.

[Stage 1, low energy μ

] The rst observation of the emission of low energy positive μ

was

performed by Harshman et al. at TRIUMF. They could extract the so-called epithermal μ

with a

kinetic energy less than 10eV from solid lithium uoride (LiF), quartz, and copper with an ef-

ciency

of (1.6 ± 0.25) × 10

−7

per incident surface muon (Harshmann et al., 1986a,b).

[Stage 2, low energy μ

] Soon after this rst successful extraction of the epithermal μ

, Harshman

et al. also succeeded in observation of the epithermal muons below ∼10eV with a tail extending to

higher energies, from solid neon (Ne), argon (Ar), krypton (Kr), and xenon (Xe) moderators exposed

to the surface muons. Among the moderators, Ar was discovered to produce the highest yield of 10

−5

low

energy μ

per incident surface muon, as shown by Harshmann et al. (1986a,b).

196 Charged Particle and Photon Interactions with Matter

[Stage 3, low energy μ

] At Paul Scherrer Institute (PSI), Morenzoni et al. (1994) succeeded in

the rst measurement of the spin polarization of the low energy muon beam emitted from solid Ar

and Kr, utilizing the world’s strongest direct current (DC, not pulsed) surface muon beam. They

demonstrated that the low energy μ

beam generated through the cryogenic moderation method

using the van der Waals solids, such as Ar and N

, is a very powerful spin-polarized probe and

that there is no observable spin depolarization during the slowing-down process in the cryogenic

moderator.

The importance of this discovery should be stressed, since not only did they develop the practical

experimental technique of the low energy muon generation through the cryogenic moderation of the

surface muon beam, but also opened and established, in reality, various kinds of scientic applica-

tions,

such as surface and interface studies, using the low energy μ

[Stage 4, low energy μ

] Recently, Prokscha et al. (2008) constructed the new μE4 beamline

dedicated for the low energy μ

generation at PSI. With a solid-angle acceptance of 135msr, they

obtained the highest ux of 4.2 × 10

surface muons s

−1

. By constructing the most intense DC sur-

face muon beam channel, they have now prepared an intense and excellent low energy μ

source at

PSI

and opened up many new applications for the low energy muons.

8.6.1.1

experimental

echnique

and Features of the l

nergyμ

beam

through

the Cryogenic m

oderation

ethod

At PSI, the low energy μ

beams had been developed at πE1 and πE3 beam lines (Morenzoni etal.,

1994) and now have been extended at the μE4 by Prokscha et al. (2008). The principle of the experi-

mental setup to obtain epithermal low energy μ

through the cryogenic moderation method at PSI

beautifully simple and is shown in Figure 8.20 (Morenzoni et al., 1994).

The

intense surface muon beam is introduced into the cryogenic moderator consisting of a high-

purity (99.999%) aluminum (Al) support foil of 250mm thickness and a thin layer of deposited solid

Ar or N

. In the case of Ar or N

(Ne), about 5 × 10

−5

(1.5 × 10

−4

) of the surface muons are converted

into the epithermal μ

. The epithermal μ

emitted from the moderator are then re-accelerated up

to 20kV and transported and focused by electrostatic Einzel lenses and a mirror into the sample.

On the way towards the sample, the accelerated μ

pass through a carbon foil of 10 nm thickness,

which provides a trigger signal for the TOF measurements (implantation time) at DC muon facility.

The use of such a trigger is unavoidable, but has the unwanted consequence of introducing a small

amount of energy and temporal spread. Finally, the kinetic energy of the low energy μ

(implanta-

tion energy) can be adjusted from 0.5 to 30 kV, by applying an accelerating or decelerating potential

to 12

to the sample.

8.6.1.2

yield

of the l

nergy

uons

at psi

According to Prokscha et al. (2008), at the newly built μE4 beam channel, the maximum 16 × 10

low energy μ

−1

at the Ne production target were obtained and 7.7 × 10

−1

were extracted at the

sample.

8.6.1.3 aspects

of the Charged p

article

nteractions

on the l

nergy

generation

The energy distribution of the low energy μ

generated through the cryogenic moderation method

has a peak at around 15eV with a tail extending to higher energies. In that sense, the low energy μ

through the cryogenic moderation method can be regarded as an epithermal μ

with the full spin

polarization. The mechanism of the emission of the epithermal μ

may include important features

of the “Charged Particle Interactions with Matter.” In the matter, the slowing down of μ

can be

proceeded by (1) Bethe–Bloch ionization, (2) cyclic charge-exchange muonium (designated as Mu,

consisting of a bound μ

and an e

−

, effectively a hydrogen-like atom) formation and break-up pro-

cess,

and (3) thermalization (Senba et al., 2006).

However,

in the wide-band-gap insulators such as Ar, N

, or Ne with band-gap energy of

between 11 and 22 eV, once μ

reached a kinetic energy of the order of their band-gap level, the

Muon Interactions with Matter 197

processes (2) and (3) are signicantly suppressed. At the last process of (2), epithermal μ

may

escape from the ionization track where excess e

−

are abundant, resulting in suppressing Mu forma-

tion and efcient emission of epithermal μ

into vacuum. Prokscha et al. (2008) examined Mu and

diamagnetic muon fraction in Ar, N

, and Ne, etc. as a function of implantation energy utilizing

the low energyμ

. In those cryogenic solid samples, Mu fraction was found to be suppressed near

the surface, in contrast to the diamagnetic muon fraction increasing near the surface, where the

excess e

−

are not abundant. These views occurring in the ionization track can also be reconrmed

by the dependence of the external electric eld on the Mu and μ

amplitudes in the solid N

20 K by Storchak et al. (1999). Both experimental results show the importance of charged particle

interactions with matter, in particular the behavior of excess e

−

in the ionization track.

Mirror

Muon spin

Surface muon

beam

(E = 4 MeV)

Muon spin

Trigger

detector

Helmholtz

coils

Positron

counters

Cryostat

Cryogenic moderator

(solid, Ar, N

, or Ne)

Muon momentum

Figure 8.20 The principle of the experimental setup for epithermal low energy μ

through the cryogenic

moderation method developed at PSI (Morenzoni et al., 1994; Prokscha et al., 2008). The intense surface

muon beam is introduced into the cryogenic moderator consisting of a high-purity (99.999%) aluminum (Al)

support foil of 250mm thickness and a thin layer of deposited solid Ar or N

. The epithermal μ

emitted from

the moderator are then re-accelerated up to 20 kV and transported and focused by electrostatic Einzel lenses

and

a mirror into the sample.

198 Charged Particle and Photon Interactions with Matter

8.6.2 generation of ultraSlow μ

through the reSonant ionization of therMal Mu

The second method is the ultraslow muon generation through the resonant ionization of thermal

Mu atoms, developed at KEK (High Energy Accelerator Research Organization) and RIKEN-RAL

(RIKEN Muon Facility of Rutherford Appleton Laboratory) pulsed muon facilities. This method

has

been developed by the following ve stages:

[Stage 1, ultraslow μ

] Thermal muonium formation in vacuum.

[Stage 2, ultraslow μ

] Experiments for the precise measurement of Mu’s 1s-2s state for the pur-

pose

of the quantum electro dynamics (QED) test at KEK-MSL (Muon Science Laboratory).

[Stage

3, ultraslow μ

] The ultraslow muon generation by 1s-2p-unbound transitions, placing a

production target W in a primary proton beam at KEK-MSL.

[Stage

4, ultraslow μ

] The ultraslow μ

generation by 1s-2p-unbound transitions, utilizing an

intense

surface muon beam at RIKEN-RAL.

[Stage

5, ultraslow μ

] Japan Proton Accelerator Research Complex (J-PARC) ultraslow μ

project.

[Stage 1, ultraslow μ

] When surface muons are stopped at the hot tungsten (W) in the ultra high

vaccum (UHV) condition, thermal energy Mu atoms were found to be evaporated into vacuum

from a clean and hot W foil. The total Mu yield was found to increase with increasing temperature

and about 0.04Mu yield per stopped surface muons (i.e., efciency of 4%) was observed at 2300K,

according to the Mills et al. (1986) experiments. Note that it is this extremely high efciency of

converting surface muons to ∼0.2eV thermal energy muons (albeit bound to an electron) that can be

exploited

for low energy muon generation through the cryogenic moderation.

[Stage

2, ultraslow μ

] The second stage consisted of the experiments for the precise measure-

ment of Mu’s 1s-2s transition frequency for the purpose of the precise QED test, performed by

Chuet al. (1988). Since Mu consists of muon (lepton) and electron (lepton) pair compared with

hydrogen that is a pair of hadrons (consisting of three quarks) and electron (lepton), Mu is con-

sidered to be the ideal and simplest system to test QED theory. In this experiment, thermal Mu

atoms were produced in vacuum by utilizing a SiO

powder sample. The 1s-2s transition as well

as the 2s-unbound transitions were induced by light from a frequency doubled pulsed dye laser.

The 1S(F=1)–2S(F=1) transition frequency was experimentally determined to be within 300MHz

of the QED theory prediction (Chu et al., 1988; Meyer et al., 2000). In these experiments, for the

rst time, the ultraslow μ

was generated by the laser resonant ionization of Mu, although it was

not intended.

[Stage 3, ultraslow μ

] The third stage consisted of the ultraslow μ

generation via 1s-2p-unbound

two-photon ionization of thermal Mu at KEK. In this step, boron nitride (BN) followed by W target

was installed in the proton line. In BN, π production and πμ decay takes place. In W, a fraction of

decayed μ

stop and diffuse into the rear surface of W, and then pick up electrons at surface, fol-

lowing which Mu atoms evaporate into vacuum. The Mu atoms that are evaporated from W into

vacuum are then ionized by intense laser pulses to generate the ultraslow μ

. This concept, a new

method

to generate the ultraslow μ

, was successfully established by Nagamine et al. (1995).

[Stage 4, ultraslow μ

] The fourth stage consisted of the experiments at RIKEN-RAL at ISIS

in UK where very intense pulsed surface muon beam is available. Here, the experiment was setup

directly at the beamline delivering the intense surface muon beam, taking the advantage of the fact

that the intensity of the primary proton beam at ISIS of 200 μA is about 40 times larger than that of

KEK-MSL (Miyake et al., 2000). At the RIKEN-RAL muon facility, nally, extraction of 20 ultra-

slow μ

−1

out of 1.2 × 10

−1

surface muons was achieved with an overall efciency comparable to

the

cryogenic moderator method and many unique parameters.

[Stage

5, ultraslow μ

] The fth step is the ultraslow muon source at J-PARC. The muon science

facility (MUSE), along with the neutron, hadron, and neutrino facilities, is one of the experimental

areas of J-PARC, which was approved for construction at the Tokai JAEA site. The MUSE facil-

ity is located in the Materials and Life Science Facility (MLF), which is a building integrated to

Muon Interactions with Matter 199

include both neutron and muon science programs. Construction of the MLF building was started

in the beginning of 2004, and the rst muon beam was delivered in the autumn of 2008. A super

omega muon channel with a large acceptance to extract the world’s strongest pulsed surface muon

beam is planned to be installed. Its goal is to extract 4 × 10

surface muons s

−1

for the generation

of the intense ultraslow μ

, utilizing laser resonant ionization of Mu by applying an intense pulsed

VUV laser system. As a maximum, 1 × 10

ultraslow muons s

−1

will be expected, which will allow

for the extension of μSR into the eld of thin lm and surface science (Miyake et al., 2009). All the

experimental apparatus that have been installed at RIKEN-RAL muon facility are planned to be

transferred

to J-PARC when the super omega muon beam channel is ready at J-PARC.

8.6.2.1

the

ltraslow

generation by resonant ionization of mu

The ultraslow pulsed muons are generated by the resonant ionization of thermal muonium atoms

generated from the surface of a hot W foil, placed at the intense surface muon beam line. In order to

efciently ionize the Mu near the W surface, a resonant ionization scheme via the {1S-2P-unbound}

transition was adopted. This requires a laser system to generate Lyman-α photons (in the vacuum

ultraviolet (VUV) region around 120nm) and 355nm photons (for the ionization step from the 2P

state). Since there are only very few solids that are partly transparent in VUV region, the genera-

tion of the 120nm photons is the most challenging part of such experiment. For the experiments

both at KEK-MSL and at RIKEN-RAL, a very efcient technique of nonlinear up-conversion in

Kr gas, the so-called resonant four-wave frequency mixing (ω

VUV

= 2 ω

− ω

), has been adopted.

This wave mixing technique generates the Lyman-α photon through a parametric process of add-

ing energies of two 212.55nm photons (ω

) and subtracting energy of one tunable infrared photon

(ω

). This allows the generation of a VUV pulse that is easily tunable and has the bandwidth of

∼200 GHz required to cover the Doppler broadening of the Mu atoms moving at thermal veloci-

ties corresponding to 2000 K. The 212.55nm UV beam is generated as a fourth harmonic of the

fundamental laser operating at 850nm. This single-mode 850nm light with a bandwidth of 0.5–

1.0 GHz is generated from an OPO system (Continuum Mirage800) and amplied by series of

Ti:sapphire ampliers. The output energy of the single-mode beam at 850nm is as high as 300mJ

−1

at 25 Hz repetition rate and pulse duration of 5ns. The amplied 850nm light is quadrupled by

using two β-Ba

crystals, generating two beams at 212.55nm wavelength with pulse energy of

10 mJ each. The difference tunable infrared beam was generated by a broadband OPO laser system

(Continuum Mirage3000). Finally, in order to ionize the Mu atom from the excited 2P state, a third

harmonic of a Nd:YAG laser (Continuum Powerlite 9025) with a wavelength of 355nm was used

(Miyake et al., 1995).

Figure 8.21 (top) shows a resonant ionization scheme via the 1s-2p-unbound transition for the

hydrogen atom isotopes 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

5P[1/2,0] state in krypton, subtracted by a photon with a tunable difference wavelength.

Experiments have been performed using “slow-ion optics,” which consists of an immersion lens

(SOA), a magnetic bend for mass separation, an electrostatic mirror, and ve sets of electrostatic

quadrupoles. Charged particles ionized by the laser pulses are extracted by the SOA lens with an

acceleration voltage of 9.0kV (20 kV to be prepared), and transported to a micro-channel plate

(MCP) detector located about 3 m from the target. Any ions produced at the W target region can

be identied through the mass/charge (Q) ratio by setting the bending magnet in the ion optics,

and by observing the time-of-ight (TOF) spectrum, consequently minimizing the background

signicantly. Additionally, the electrostatic deector selects the energy of the particles that are

transported to the sample, thus signicantly suppressing the background. The laser pulses are

delayed by typically 400ns relative to the surface muon pulse to allow time for Mu to move away

from the target, since the mean thermal velocity in only 20 mm μs

−1

. A high-purity (99.9999%)

W foil with 50 μm thickness (obtained from Metallwerk Plansee GmbH) is placed inside the SOA

target chamber. The W foil is heated up to 2300K by a pulsed DC current that is turned off for