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

Подождите немного. Документ загружается.

160 Charged Particle and Photon Interactions with Matter

enhancement and inhibition effects. The electron scavengers capture the excess electrons and the

Ps formation is inhibited. Simultaneously, the electron scavengers inhibit the cation–excess electron

recombination, and the cation concentration in the positron spur is enhanced. This is the reason why

the electron scavenging effect is not visible for the fourth component around 0.01M in Figure 7.26.

Figure 7.27 indicates the fraction of the fourth components in all of the o-Ps components, that is, the

sum of the fourth and the longest-lifetime components (Hirade and Mogensen, 1993b: 127; 1994: 491).

It is smaller for CS

and C

. These are not just electron scavengers but also Ps formation enhancers.

These electron scavengers capture electrons and the cation–electron recombination is inhibited, but

freely moving positrons can arrive at these electron scavengers to pick off electrons to form Ps. The

positron formed by the Ps oxidation by cations can also arrive at these scavengers to form Ps once

more. Three-fourths of newly formed Ps will be o-Ps, and hence the oxidation is not visible.

The other important feature is a spin conversion reaction of o-Ps by radical species, such as cations

or solvated electrons. p-Ps caused by the spin conversion reaction annihilates intrinsically with a life-

time of about 125ps. It can be one of the reasons of the appearance of the fourth-lifetime component.

The temperature dependence of the lifetime of the o-Ps pick-off annihilation in water showed a

strange tendency. The o-Ps pick-off annihilation lifetime should be larger at higher temperatures, as

explained in Section 7.3.1. However, it is shorter at higher temperatures in water (Kotera et al., 2005:

184). This could be explained by the reaction between o-Ps and spur species (Stepanov et al., 2007:

90). There is some possibility of a reaction of geminate pairs of o-Ps and a radical in the positron

spur. The geminate pair reactions show quantum beats caused by the spin-dependent reactions, and

the

details are given in Section 7.6.8.

7.6.8 poSitroniuM aS a probe of free radicalS

AMOC measurements are a very useful tool to investigate the reactions of positron and Ps. As

shown in Figure 7.28, AMOC can detect Ps oxidation, p-Ps/o-Ps spin conversion, and complex for-

mation and positron reactions (Castellaz et al., 1996: 457). An example of p-Ps/o-Ps spin conversion

was indicated in Figure 7.29 (Stoll et al., 1995: 17). While it is very difcult to know the existence of

the p-Ps/o-Ps spin conversion by PAL, S(t) obtained by AMOC is a very useful tool for this purpose.

Recently, a new method for the use of Ps reactions has been established by Hirade (2009a: 132). It

is possible to observe the quantum beats caused by the hyperne coupling in radicals. The complex

formation and the oxidation of Ps should show spin dependence. The complex formation, that is, the

radical reaction, can occur while the two unpaired electrons are in a singlet state, because both the

0.4

0.35

0.3

0.25

Hexane/CCl

Hexane/CS

Hexane/C

Hexane/SF

0.2

0.15

0.1

0 0.001 0.01

Concentration (M)

/(I

)

0.1 1 10

Figure 7.27 Effects on the fraction of short-lived o-Ps, I

, in whole o-Ps, I

+ I

, by electron scavengers.

(Reprinted

from Hirade, T. and Mogensen, O.E., J. Phys. IV C4, II(3), 127, 1993b. With permission.)

Positron Annihilation in Radiation Chemistry 161

electrons will be in the same orbital after the reaction. The same can be said for the oxidation. Ps

is a bound state of an electron and a positron, that is, it has an unpaired electron, which means that

Ps is a free radical. This electron has been one of the excess electrons in the terminal spur of the

positron track. Therefore, there is a radical with an unpaired electron that has spin correlation with

the electron in Ps, that is, the radical and the Ps are a geminate pair. There is one more possibility of

reaction between the Ps and the radical, that is, the spin conversion reaction, as mentioned above. If

the Ps is o-Ps, it has the longest lifetime and it is very easy to detect it, as indicated in Figure 7.29.

0.55

0.50

0.0 2.0 4.0

Positron age (ns)

(ox= oxidizing)

6.0

0.55

0.50

0.0 2.0 4.0

Positron age (ns)

6.0

0.55

0.50

0.0 2.0 4.0

Positron age (ns)

(c= complex forming)

(p = paramagnetic)

6.0

0.55

0.50

0.0 2.0 4.0

Positron age (ns)(d)(c)

(a) (b)

6.0

Ps+ M

–

+ A

–

]

p-Ps(o-Ps) + M

–—p -Ps+–—o-Ps + M

Figure 7.28 The age dependence of the line-shape functions, S(t), for different chemical reactions. Solid

lines: Ps formation without reactions. Dashed lines: Inclusion of reactions as indicated in the gures: (a) oxidation

of Ps, (b) spin conversion of Ps, (c) Ps complex formation, and (d) e + bound-state formation. (From Castellaz, P.,

J. Radioanal. Nucl. Chem., 210(2), 457, 1996, Figure 3. With permission.)

0.6

0.5

0.6

0.5

0 2 4

Age t (ns)(a) (b)

Age t (ns)

6 8 0 2 4 6 8

Figure 7.29 St(t) for 0.1 M HTEMPO in benzene obtained by AMOC measured at 266K (a, solid) and

313K

(b, liquid). (Reprinted from Siegle, A. et al., Appl. Surf. Sci., 116, 140, 1997. With permission.)

162 Charged Particle and Photon Interactions with Matter

The geminate radical–Ps reaction is a diffusion-controlled reaction, and the radical reaction, that is,

the complex formation or the oxidation, and the spin conversion reaction are the competitive reac-

tions. When the probability of one reaction goes down, that of the other goes up. Now the radical

reaction

of the geminate radical–Ps pairs depends on the spin state of the two unpaired electrons.

The

unpaired electron in the free radical, such as the hydroxyl radical in water, will have Larmor

precession because of the hyperne coupling. In liquids, only isotropic hyperne coupling, that is,

the Fermi contact term, is detectable. The Larmor precession frequency caused by a proton having

a spin of 1/2 will be about 50–500MHz. Ps has a very large hyperne coupling constant, 203GHz

in vacuum. A positron spin of 1/2 gives the Larmor precession frequency of the electron in Ps, that

is, 101.5GHz. Although it is a value for Ps in vacuum, the frequency is very fast. Now, we applied

500 MHz for the radical and 101.5GHz for Ps as an example. The geminate radical pair is in the

singlet state initially, and these Larmor precessions make a transition between the singlet state and

the triplet state. There are two frequencies of the singlet–triplet transition, 101.5GHz + 500MHz

and 101.5GHz − 500MHz. Therefore, the observable singlet-state probability will have a swell, as

shown in Figure 7.30. There is no fast oscillation at the positron ages of 0.5, 1.5, 2.5 ns,…, and half

of the radical–Ps pairs are in the singlet state. Therefore, more than half of the radical–Ps pairs

perform the p-Ps/o-Ps spin conversion reaction that can be detected by the AMOC measurement.

On the other hand, the singlet-state probability at the swells, that is, at 0, 1, 2ns,…, oscillates with

about a 10ps cycle. Although the average singlet-state probability is 0.5, most of the radical–Ps pairs

will be in a singlet state every 10ps at the swells. It means that the possibility of the radical reac-

tions, such as complex formation or oxidation, at the swells will be more than between the swells,

and hence the probability of the p-Ps/o-Ps spin conversion reaction will be less at the swells. Hence,

there will be beats of enhancement on the S(t) caused by the spin conversion of o-Ps between the

swells, that is, at the positron ages of 0.5, 1.5, 2.5 ns,…, in the case of this example, with 500MHz

for the radical and 101.5GHz for Ps. S(t) were measured in water at 18°C and 25°C, and the quan-

tum beats caused by the spin conversion of p-Ps/o-Ps were successfully observed, as in Figure 7.31

(Hirade, 2009a: 132). The hyperne coupling constants of the hydroxyl radicals in water were 870

and 758MHz at 18°C, and 816 and 656MHz at 25°C (Hirade, 2009a: 132). These large hyperne

coupling constants indicate that it is not a simple hydroxyl radical. The quantity of the isotropic

hyperne coupling constant, that is, the Fermi contact term, of the OH radical is 73.25MHz, while

that of the OH–H

O complex is 155.3MHz (Brauer et al., 2004: 420). The large hyperne coupling

constants are probably caused by the radicals in water clusters or water cluster cation radicals. The

beats appeared at the expected positron ages, and this indicates that the structures are quite stable

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1.00

0.75

0.50

0.25

0.00

Time (ns)

Singlet-state probability

Figure 7.30 Time dependence of singlet-state probability of the geminate radical pair with Larmor preces-

sion

frequencies, 500

MHz

for the radical and 101.5

GHz

for o-Ps.

Positron Annihilation in Radiation Chemistry 163

at 0–6ns. If there are many different structures that exist continuously, there will be many different

hyperne couplings, and so the beats cannot be observed. This means that there are only two struc-

tures and these show almost no changes up to about 6ns. Every structure changes continuously with

the elevation of temperature. The hyperne coupling constants are smaller at higher temperatures.

The fourth-lifetime component was explained in Section 7.6.7. It is mainly caused by the reaction

of o-Ps and cations. It is found in many liquids. This means that the quantum beats can be measured

in many liquids and the direct observation of cation radicals is possible by this method. In the case of

water, the hyperne coupling constants seem to depend on the temperature. However, there will not

be large temperature effects on the hyperne coupling constants for radicals in other liquids. Figure

4 in Stoll et al. (1995: 17) shows S(t) for n-hexane, and it is clear that there are reactions between o-Ps

and cation radicals (Levay and Mogensen, 1980: 131; 1993a: 249; 1993b: 127; 1994: 491). The quantum

beats appeared at around 2.7 and 3.8ns. The spin state of the geminate pair, o-Ps and n-hexane cation

radical, is a singlet at the positron age of zero; thus, the ages for having the beats are quite reasonable.

7.7 positron annihilation on moleCules

The most important process that we can derive from positron studies is annihilation. Positron anni-

hilation can provide information of the interaction between positrons and molecules or atoms in gases.

This information is very important in many areas of science and technology. Annihilation γ-rays from

10–1

0.38

0.40

0.42

S(t)

0.44

0.46

Positron age t (ns)

3 4 5 6

10–1

0.40

0.42

S(t)

0.44

0.46

Positron age t (ns)

3 4 5 6

Figure 7.31 S(t) curves obtained by AMOC for pure water after nitrogen gas bubbling. The upper curve is

measured at 18°C and the lower curve is measured at 25°C. (From Hirade, T., Chem. Phys. Lett., 480, 132, 2009a.

With permission.)

164 Charged Particle and Photon Interactions with Matter

the universe are becoming a very interesting object for astrophysics (Milne, 2006: 548). At the incident

positron energies below the threshold of Ps formation by the Ore model (Ore, 1949), the annihilation

rates with some molecules are far in excess of the expected rates by simple two-body collisions (Paul

and Saint-Pierre, 1963: 493). Many experiments and theoretical studies have been conducted since the

initial experiments (Paul and Saint-Pierre, 1963: 493). The positron–molecule annihilation, studied

by positrons with a well-controlled and tunable energy, was sufcient to resolve structures on the

scale of molecular vibrational energies (Gilbert et al., 1997: 1944). Subsequently, large resonances in

annihilation rates, Z

eff

, were discovered, as shown in Figure 7.32 (Gilbert et al., 2002: 043201). Z

eff

the measured annihilation rate divided by that calculated for an uncorrelated electron gas at a density

equal to the molecular number density. If there is no correlation between the molecular electrons and

the positron, Z

eff

, is the number of electrons in molecule.

20,000

10,000

(scaled)

eff

10,000

5,000

1000

500

0.0 0.1 0.2 0.3

Energy (eV)

0.4 0.5

(a)

(b)

(c)

Figure 7.32 Positron annihilation rate, Z

eff

, for (a) butane, (b) propane, and (c) ethane, as a function of

positron energy, ε, in the range of 50 < ε < 450meV. Vertical bars along the abscissas indicate the strongest

infrared-active vibrational modes. Arrows on the ordinate indicate Z

eff

for a Maxwellian distribution of posi-

trons at 300K. Z

eff

for d-butane is shown by the dashed curve in (a), with the amplitude normalized, and the

energy scaled by the appropriate reduced-mass factor. The annihilation rate for 2,2-diuoropropane (C

)

is indicated by the dashed curve in (b). (Reprinted from Gilbert, S.J. et al., Phys. Rev. Lett., 88(4), 043201,

2002.

With permission.)

Positron Annihilation in Radiation Chemistry 165

Recently, it has been understood that this phenomenon is due to positron attachment to molecules.

This attachment enhances the overlap of the positron with molecular electrons, which increases the

annihilation rates. The attachment is caused by vibrational Feshback resonances (Young and Surko,

2009: 9).

reFerenCes

Anderson, C. D. 1933. The positive electron. Phys. Rev. 43: 491–494. http://link.aps.org/abstract/PR/v4355/p491

Brandt, W., Coussot, G., and Paulin, R. 1969. Positron annihilation and electronic lattice structure in insulator

crystals.

Phys. Rev. Lett. 23: 522–524.

Brauer,

C. S., Sedo, G., Grumstrup, E. M., Leopold, K. R., Marshall, M. D., and Leung, H. O. 2004. Effects of

partially quenched orbital angular momentum on the microwave spectrum and magnetic hyperne split-

ting

in the OH–water complex. Chem. Phys. Lett. 401(4–6): 420–425.

Brusa,

R. S., Duarte Naia, M., Margoni, D., and Zecca, A. 1995. Positron mobility in polyethylene in the

60–400

K temperature range. Appl. Phys. A 60: 447–453.

Cassidy,

D. B., Deng, S. H. M., and Mills, A. P. 2007. Evidence for positronium molecule formation at a metal

surface.

Phys. Rev. A 76: 062511.

Castellaz,

P., Major, J., Mujica, C., Schneider, H., Sebger, A., Siegle, A., Stoll, H., and Billard, I. 1996. Chemical

reactions of positronium studied by age-momentum correlation (AMOC) using a relativistic positron

beam.

J. Radioanal. Nucl. Chem.,

Articles,

210(2): 457–467.

Chalermkarnnon,

P., Shishido, I., Yuga, M., Araki, H., and Shirai, Y. 2002. b+-g Coincidence positron life-

time spectrometer with positron energy selection by electromagnetic lens. J. Jpn. Inst. Met. 66(10):

1004–1008.

Consolati, G., Gerola D., and Quasso, F. 1991. An unusual three-quantum yield from positrons annihilated in

benzene.

J. Phys.: Condens. Matter 3: 7739–7742.

Consolati,

G., Gerola, D., and Quasso, F. 1992.

positron annihilation study in some amorphous scintillators.

Z. Phys. B: Condens. Matter

88: 131–133.

Coussot,

G. 1970. Contribution a l´etudu de la structure electronique des isolants par annihilation du positon.

PhD

thesis, Faculté des Sciences d’Orsay, Universite Paris-Sud, Orsay, France.

Crowell

R. A. and Bartels D. M. 1996. H

O/D

O isotope effect in geminate recombination of the hydrated

electron.

J. Phys. Chem. 100: 17713–17715.

Dirac,

M. 1930.

Annihilation

of electrons and protons. Proc. Camb. Philos. Soc. 26: 361–375.

Dull,

T. L., Frieze, W. E., Gidley, D. W., Sun J. N., and Yee, A. F. 2001. Determination of pore size in mesopo-

rous

thin lms from the annihilation lifetime of positronium. Phys. Chem. B 105: 4657–4662.

Duplatre,

G. and Jonah, C. D. 1985. Reactions of electrons in high-concentration water solutions—A compari-

son between pulse-radiolysis and positron annihilation lifetime spectroscopy data. Radiat. Phys. Chem.

24(5/6):

557–565.

Eldrup,

M. 1976.

Vacancy

migration and void formation in g-irradiated ice. J. Chem. Phys. 64: 5283–5290.

Eldrup,

M., Lightbody, D., and Sherwood, J. 1980. Studies of phase transformation in molecular crystals using

the

positron annihilation technique. Faraday Discuss. Chem. Soc. 69: 175.

Eldrup,

M., Lightbody, D., and Sherwood, J. N. 1981. The temperature dependence of positron lifetimes in

solid

pivalic acid. Chem. Phys. 63: 51–58.

Fukaya,

Y., Kawasuso, A., and Ichimiya, A. 2009. Inelastic scattering processes in reection high-energy posi-

tron

diffraction from a Si(111)-7×7 surface. Phys. Rev. B 79: 193310.

Gee,

N. and Freeman, G. R. 1989. Electron and ion mobility in carbon disulde liquid from 163 to 501K.

Chem. Phys.

90(10): 5399–5405.

Gilbert,

S. J., Kurz, C., Greaves, R. G., and Surko, C. M. 1997. Creation of a monoenergetic pulsed positron

beam.

Appl. Phys. Lett. 70: 1944–1946.

Gilbert,

S. J., Barnes, L. D., Sullivan, J. P., and Surko, C. M. 2002. Vibrational-resonance enhancement of

positron

annihilation in molecules. Phys. Rev. Lett. 88(4): 043201.

Goworek,

2007. Free volumes in solids under high pressure. Radiat. Phys. Chem. 76: 318–324.

Hirade,

T. 1995. Positronium formation in H

O, D

O and HDO mixture. Mater. Sci. Forum 175–178: 675–678.

Hirade, T.

1996.

The

study of the electron-positron pair in CS

. Bull. Chem. Soc. Jpn. 69(8): 2153–2157.

Hirade, T.

2003. Positronium formation in low temperature polymers. Radiat. Phys. Chem. 68: 375–379.

Hirade,

2007. Connections between radiation and positronium chemistry. Radiat. Phys. Chem. 76: 84–89.

Hirade,

T. 2009a. Age-momentum correlation measurements of positron annihilation in water: Possibility of

quantum

beats on ortho-positronium reactions. Chem. Phys. Lett. 480: 132–135.

166 Charged Particle and Photon Interactions with Matter

Hirade, T.

2009b. Positronium formation in room temperature ionic liquids. Mater. Sci. Forum 607: 232–234.

Hirade,

T. and Mogensen, O. E. 1993a. Dependence of the yield of the short-lived ortho-Ps state on the concen-

tration

of CCl

in hexane. Chem. Phys. 170: 249–256.

Hirade, T. and Mogensen, O. E. 1993b. Effects of scavengers on short-lived ortho-Ps. J. Phys. IV C4, II, 3:

127–130.

Hirade, T. and Mogensen, O. E. 1994. Secondary reaction of Ps in the positron spur. Hyperne Interact. 84:

491–498.

Hirade, T., Wang, C. L., Maurer, F. H. J., Eldrup, M., and Pedersen, N. J. 1998. Visible light effect on posi-

tronium formation in PMMA at low temperature. In Abstract book for The 35th Annual Meeting on

Radioisotopes in the Physical Science and Industries,

June 30–July 1,

Tokyo,

Japan, p. 89.

Hirade,

T., Maurer, F. H. J., and Eldrup, M. 2000. Positronium formation at low temperatures: The role of

trapped

electrons. Radiat. Phys. Chem. 58: 465–471.

Hirade,

T., Suzuki, N., Saito, F., and Hyodo, T. 2007. Reactions of free positrons in low temperature polyethyl-

ene-delayed

Ps formation and positron localization. Phys. Status Solidi (c) 4, 10: 3714–3717.

Hyodo,

T. and Takahashi, Y. 1977. Evidence for positronium-like states in NaF and NaCl. J. Phys. Soc. Jpn.

42:

1065–1066.

Ito,

K., Nakanishi, H., and Ujihira, Y. 1999. Extension of the equation for the annihilation lifetime of ortho-

positronium

at a cavity larger than 1

in radius. J. Phys. Chem. B 103: 4555–4558.

Jacobsen,

F. M., Mogensen, O. E., and Trumpy, G. 1982. Correlation of positronium yield with excess electron

mobility

in liquid neopentane. Chem. Phys. 69: 71–80.

Jansen,

P. and Mogensen, O. E. 1977. Further studies of the spur process of positronium formation in mixtures

organic liquids. Chem. Phys. 25: 75–86.

Jean,

Y. C. 1993. Positron spectroscopy of solids. In Proceedings of the International School of Physics “Enrico

Fermi”

Course CXXV,

Dupasquier and

P. Mills Jr. (eds),

Varena

on Lake Como, pp. 569–571.

Jonah,

C. D. and Chernovitz, A. C. 1990. The mechanism of electron thermalization in H

O, D

O, and HDO.

Can. J. Phys.

68: 935–939.

Kasai,

J., Hyodo,

T.,

and Fujiwara, K. 1988. Positronium in alkali halides. J. Phys. Soc. Jpn. 57: 329–341.

Katoh,

R., Yoshida, Y., Katsumura, Y., and Takahashi, K. 2007. Electron photodetachment from iodide in ionic

liquids

through charge-transfer-to-solvent (CTTS) band excitation. J. Phys. Chem. B 111: 4770–4774.

Kawasuso,

A. and Okada, S. 1998. Reection high energy positron diffraction from a Si (111) surface. Phys.

Rev. Lett.

81: 2695–2698.

Kindl,

P. and Reiter, G. 1987. Investigations on the low-temperature transitions and time effects of branched

polyethylene

by the positron lifetime technique. Phys. Status Solidi (a) 104: 707–713.

Kobayashi,

Y. 1992. Pressure dependence of ortho-positronium lifetimes in molecular liquids. Ber. Bunsen-

Ges.:-Phys. Chem. Chem. Phys.

96, 12: 1869–1872.

Komuro,

Y., Hirade, T., Suzuki, R., Ohdaira, T., and Muramatsu, M. 2007. Positronium formation in fused

quartz:

Experimental evidence of delayed formation. Radiat. Phys. Chem. 76: 330–332.

Kotera,

K., Saito,

T.,

and Yamanaka,

2005. Measurement of positron lifetime to probe the mixed molecular

states

of liquid water. Phys. Lett. A 345: 184–190.

Levay,

B. and Mogensen, O. E. 1977. Correlation between the inhibition of positronium formation by scaven-

ger molecules, and chemical reaction rate of electrons with these molecules in nonpolar liquids, J. Phys.

Chem. 81:

373–377.

Levay

B. and Mogensen, O. E. 1980. Positron spur reactions with excess electrons and anions in liquid organic

mixtures

of electron acceptors. Chem. Phys. 53: 131–139.

Milne, P.

2006. Distribution of positron annihilation radiation. New Astron. Rev. 50, 7–8: 548–552.

Mogensen,

O. E. 1974. Spur reaction model of positronium formation. J. Chem. Phys. 60: 998–1004.

Mogensen,

O. E. 1994. Positron states between positronium and “free positron” states in condensed matter.

Hyperne Interactions,

84, 1: 377–387.

Mogensen,

O. E. 1995. Positron Annihilation in Chemistry. Springer, Berlin, Germany.

Mogensen,

O. E. and Eldrup, M. 1977. Positronium Bloch function, and trapping of positronium in vacancies,

ice. Risø Report No. 366.

Mogensen,

O. E. and Eldrup, M. 1978. Vacancies in pure ice studied by positron annihilation techniques.

J.Glaciol. 21, 85: 85–99.

Mogensen, O. E. and Jacobsen, F. M. 1982. Positronium yields in liquids determined by lifetime and angular

correlation

measurements. Chem. Phys. 73: 223–234.

Mogensen,

O. E., Kvajic, G., Eldrup, M., and Milosevic-Kvajic, M. 1971. Angular correlation of annihilation

photons

in ice single crystals. Phys. Rev. B 4: 71–73.

Positron Annihilation in Radiation Chemistry 167

Ohdaira, T., Suzuki, R., Mikado, T., Ohgaki, H., Chiwaki, M., and Yamazaki, T. 1997. An apparatus for high-

resolution positron-annihilation induced Auger-electron spectroscopy using a time-of-ight technique.

Appl. Surf. Sci.

116: 177–180.

Ore,

1949. Univ. of Bergen Aarb. Naturvit. Rekke 9.

Oshima,

N., Suzuki, R., Ohdaira, T., Kinomura, A., Narumi, T., Uedono, A., and Fujinami, M. 2009. Rapid

three-dimensional imaging of defect distributions using a high-intensity positron microbeam. Appl. Phys.

Lett.

94: 194104.

Paul,

L. and Saint-Pierre, L. 1963. Rapid annihilations of positrons in polyatomic gases. Phys. Rev. Lett.

11:

493–496.

Saito,

H., Nagashima, Y., Kurihara, T., and Hyodo, T. 2002. A new positron lifetime spectrometer using a fast

digital

oscilloscope and BaF

scintillators. Nucl. Instrum. Methods Phys. Res. A 487: 612–617.

Siegle, A., Stoll, H., Castellaz, P., Major, J., Schneider, H., and Seeger, A. 1997. Two-dimensional analysis of

positron

age-momentum correlation (AMOC) data. Appl. Surf. Sci. 116: 140–144.

Stepanov,

S. V., Byakov, V. M., and Kobayashi, Y. 2005. Positronium formation in molecular media: The effect

the external electric eld. Phys. Rev. B 72: 054205.

Stepanov,

S. V., Byakov, V. M., and Hirade, T. 2007. To the theory of Ps formation. New interpretation of the e

lifetime

spectrum in water. Radiat. Phys. Chem. 76: 90–95.

Stoll,

H., Koch, M., Lauff, U., Maier, K., Major, J., Schneider, H., Seeger, A., and Siegle, A. 1995. Annihilation

of incompletely thermalized positronium studied by age-momentum correlation. Appl. Surf. Sci. 85:

17–21.

Suzuki, R., Kobayashi, Y., Mikado, T., Ohgaki, H., Chiwaki, M., Yamazaki, T., and Tomimasu, T. 1991. Slow

positron pulsing system for variable energy positron lifetime spectroscopy. Jpn. J. Appl. Phys. 30:

L532–L534.

Suzuki, R., Ohdaira, T., and Mikado, T. 2000. A positron lifetime spectroscopy apparatus for surface and near-

surface

positronium experiments. Radiat. Phys. Chem. 58, 5–6: 603–606.

Suzuki,

N., Hirade, T., Saito, F., and Hyodo, T. 2003. Positronium formation reaction of trapped electrons and

free

positrons: Delayed formation studied by

AMOC.

Radiat. Phys. Chem. 68: 647–649.

Tao, S. J. 1972. Positronium annihilation in molecular substances. J. Chem. Phys. 56: 5499–5510.

Van

House, J. and Rich,

1988.

Arthur,

rst results of a positron microscope. Phys. Rev. Lett. 60: 169–172.

Wang,

C. L., Hirade, T., Maurer, F. H. J., Eldrup, M., and Pedersen, N. J. 1998. Free-volume distribution and

positronium formation in amorphous polymers: Temperature and positron-irradiation-time dependence.

J. Chem. Phys.

108 11: 4654–4661.

Young,

J. A. and Surko, C. M. 2009. Resonant positron annihilation on molecules. Mater. Sci. Forum 607: 9–16.

Zgardzinska, B., Hirade, T., and Goworek, T. 2007. Positronium formation on trapped electrons in n-heptadecane.

Chem. Phys. Lett.

446: 309–312.

169

Muon Interactions with Matter

Khashayar Ghandi

Mount Allison University

Sackville,

New Brunswick, Canada

Yasuhiro Miyake

High Energy Accelerator Research Organization

Tokai,

Japan

8.1 the interaCtion oF muons with matter in the gas phase

8.1.1 general introduction

Muons (μ

, μ

−

) occur naturally in cosmic ray showers, but not in great enough intensity for study.

Therefore, they are produced articially with MeV kinetic energies (4.1 MeV for surface muons and

larger energies for muons from decay channels) at nuclear accelerators like TRIUMF in Canada,

Rutherford Appleton Laboratory (RAL) in the United Kingdom, The Paul Scherrer Institute in

Switzerland,

and the Japan Proton Accelerator Research Complex.

the decay sequence π

→ μ

→ e

, the muon is produced 100% spin polarized from pion decay

and the (detected) positron is subsequently emitted preferentially along the muon-spin direction.

Contents

8.1 The Interaction of Muons with Matter in the Gas Phase...................................................... 169

8.1.1 General

Introduction................................................................................................. 169

8.1.2

Muon

Polarization and Its Measurements ................................................................ 170

8.1.3

Free-Radical

Formation in the Gas Phase................................................................ 176

8.2

Muon

Radiation Chemistry in Molecular Liquids ............................................................... 178

8.3

The Interaction of Muons with Supercritical Fluids.............................................................. 181

8.4 Muon

Radiation Chemistry in Ionic Liquids........................................................................ 185

8.5

Review

of the Modern Aspects of Muonium Reaction Dynamics and Free-Radical

Studies

by Muons.................................................................................................................. 186

8.5.1

Introduction

and Techniques .................................................................................... 186

8.5.2

Studies in Supercritical Fluids and Liquids.............................................................. 187

8.5.3 Studies

in the Gas Phase........................................................................................... 194

8.6

Modern

Slow Muon Beam Production Techniques.............................................................. 195

8.6.1

The

Generation of Low Energy μ

through the Cryogenic Moderation Method ..... 195

8.6.1.1 Experimental

Technique and Features of the Low Energy μ

Beam

through

the Cryogenic Moderation Method ..............................................196

8.6.1.2

Yield

of the Low Energy Muons at PSI ..................................................... 196

8.6.1.3

Aspects

of the Charged Particle Interactions on the Low Energy

Generation ............................................................................................. 196

8.6.2 Generation

of Ultraslow μ

through the Resonant Ionization of Thermal Mu......... 198

8.6.2.1 The

Ultraslow μ

Generation by Resonant Ionization of Mu ....................199

8.6.2.2 Unique

Features of the Pulsed Ultraslow μ

Beam ................................... 201

References......................................................................................................................................204