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130 Charged Particle and Photon Interactions with Matter

region above 400eV. The sharp increase near the 2p threshold for W

seems to originate from the

2p photoionization, which has a close connection with the model proposed previously in the case of

hydrocarbon molecules (Suzuki and Saito, 1985a,b, 1987; Saito and Suzuki, 1986).

The solid curve in Figure 6.18 denotes the result calculated from a model similar to that for Kr

(Saito and Suzuki, 2001b). This calculated curve agrees well with the experimental W-values in the

region of 50–1000 eV. This result postulates that the present model is semiquantitatively valid.

A slight difference between experimental and calculated W-values is seen near the 2p electron

ionization threshold. One possible reason is the assumption that energy is shared between two elec-

trons that are simultaneously ejected. This assumption causes the ionizing collisions to occur a

little more frequently than in the real situation. This effect induces lowering of calculated W-values.

Another reason probably originates from the difculty encountered in the measurement of photoion

currents. In this energy region, the photoabsorption cross section is large, and ion production takes

place inhomogeneously in the ion chamber, which possibly results in the loss of collection of photo-

ions owing to the recombination reaction of ions with electrons. This loss causes the experimental

W-value to be higher than the real one. If the recombination reaction makes a considerable effect,

the saturation curve on the electron number produced in the chamber should show a decrease at

higher

gas densities. This decrease was not found to be appreciable in the present experiment.

The

obtained at 1keV in the present study, which is 28.5 ± 1.0eV, is slightly higher than

25.8eV ± 0.6eV at 5.9 keV previously obtained (Borges et al., 1996). Since the curve of W

Figure6.18 shows a tendency of decreasing with increasing photon energy, this trend seems to take

the present W

value close to the previous one at that energy. However, Ar has the K-shell absorp-

tion edge at 3.2keV, and this edge probably yields a jump in the W

. If the jump is not large, it will

explain

the difference of W-value at the two photon energies.

The

photon W-value of Xe is shown on the absolute scale as a function of photon energy from

120 to 1000eV in Figure 6.19 (Suzuki and Saito, 2001). The data are denoted with solid circles. Bars

with hatching indicate the ionization thresholds of 4p, 4s, 3d, and 3p electrons. The data points of

open squares give the W-value for electrons, W

, which was reported earlier (Combecher, 1980). The

measured W

increases slightly near the 4p ionization thresholds, and then shows a decreasing trend

with photon energy below 670eV although the data scatter appreciably. The value of W

steeply

increases at the 3d thresholds and remains at similar values above 800 eV. Although the data seem

rise near the 3p thresholds, this feature is not decisive owing to the sizes of data scatters.

200 400 600 800 1000

W-value

Photon energy (eV)

Figure 6.19 Photon W-value for Xe as a function of photon energy. Solid circles show data by Suzuki and

Saito, and open squares are data for electrons by Combecher (1980). The solid curve represents the photon

W-values calculated using the model explained in Section 6.5.6. The bars with hatching indicate the ionization

thresholds of 4p, 4s, 3d, and 3p electrons. (Reproduced from Suzuki, I.H. and Saito, N., J. Electron Spectrosc.

Relat. Phenom. 119,

147, 2001.)

New Directions in W-Value Studies 131

The measured data of W

agree with those for electrons between 200 and 600eV, while above

700eV, W

is higher than W

. The agreement suggests that absolute values of the measured W

are

reliable. The variations near the 4p and 3d thresholds in the W

are probably due to the ionization of

these inner-shell electrons. This phenomenon is very similar to those for Ar 2p thresholds and Kr 3d

thresholds (Saito and Suzuki, 2001a,b). Inner-shell ionization increases the ratio of multiple photoion-

ization considerably, which results from Auger electron emission lling inner-shell vacancy.

The solid curve in Figure 6.19 shows the result calculated from a model similar to that for Kr

(Saito and Suzuki, 2001b). The W

value calculated has well reproduced the characteristics of the

measured W

, in particular, the steep increase at the 3d ionization thresholds. The model proposed

here is essentially valid. However, a slight discrepancy between the calculated and experimental

values is seen near 500 and 800 eV. A possible reason originates from the mixing of higher-

order radiation in the incident photon beam. The second-order radiation can yield ions in the ion

chamber about two times of the rst because the W

does not change largely in the energy region of

interest. Since the energy of the electron beam in the storage ring was lowered to 500 MeV in the

measurement of W

, the ratio of the second-order light was supposed to be extremely low. This sup-

position makes us nd another reason for the discrepancy. Scattered light with a longer wavelength

produces ions with a quantity lower than the rst-order photon, and then induces a higher W

than

real. The mixing of the scattered light can explain that experimental W

values near 800eV are

higher than the calculated results. It is suggested that a thicker lter be inserted into the incident

photon beam.

The discrepancy near 500eV may be related to the assumption of the ratio of the photoionization

shake-off process in the model calculation. This shake-off process forms many electrons simultane-

ously, and thus makes secondary ionization less efcient. A smaller number of the total electrons

is given by a larger ratio of this shake-off process, that is, a higher W

is obtained through this

assumption. Finally, the small discrepancy between the measurement and the calculation cannot be

claried

at present, and more precise work is expected to be carried out.

The

at 1keV in the present study, which is 26.8eV, is higher than the previous value of 24.2eV

at 5.9keV (Borges et al., 1996). The curve of W

in Figure 6.19 shows a tendency of decreasing with

increasing photon energy, which is similar to those for Ar and Kr (Saito and Suzuki, 2001a,b). This

trend

seems to take the present W

value close to the previous one at that energy.

6.6 outlook

As described above, we can now measure the absolute intensity of soft x-rays and the total charges

produced in rare gas atoms using the multielectrode ion chamber technique. This technique seems

to be applicable to molecular samples. However, charge states of molecules just after irradiation

have not been determined so far in most cases, because it is not certain that kinetic ions are detected

completely. Also, branching ratios for ion production and/or γ-values have not been obtained in the

soft x-ray region for the case of molecules. Photoionization shake-off processes and multiple Auger

decays have not been evaluated so far in molecules, because several fragments with some kinetic

energies complicate the situation, making measurements very difcult. At present, it is difcult to

establish a precise model for W-values of molecules in the sub-keV energy region. Thus, it is desired

that a novel technique is devised for the measurement of all photoions and that molecular data on

the charge state, that is, multiple photoionization ratio, are accumulated in the course of progress in

synchrotron

radiation researches.

the peak energies of resonance transitions into Rydberg orbitals, the absolute value of the

photon W-value for Kr has some ambiguity because the photoabsorption efciency is very high,

suggesting that a number of charges are formed near the window of the chamber. In order to cor-

rect W-values in the absolute scale, it is necessary that the charges formed are completely detected

and that the monochromator has an energy width narrower than the natural lifetime width for the

resonance

peak.

132 Charged Particle and Photon Interactions with Matter

In these years, a cryogenic radiometer has been utilized for the absolute measurement of soft

x-rays (Rabus et al., 1997; Morishita et al., 2005; Kato et al., 2010). In this instrument, all energy of

incident x-rays is received with a sensor unit and the temperature of the sensor rises. The tempera-

ture increase is detected and converted to absorbed energy. An accuracy realized with this instru-

ment is usually higher than that expected for the ion chamber technique. The metrology group of the

AIST has attempted to obtain the W-value for a mixed gas (dry air) in the keV energy region (Kato

et al., 2010). The result is almost in agreement with the electron W-value on the absolute scale and

on the energy dependence. However, the energy dependence shows a slight jump at 3.2keV, where

Ar contained in air (about 1%) has the K-shell photoabsorption edge. Using a similar model to that

described in Section 6.5.5, this jump is well reproduced. The effect of the Ar K-shell photoab-

sorption has been observed as nonlinearity by another group who utilized the gas-scintillation

proportional counter (Monteiro et al., 2003). Further, electron W-values for air have been redeter-

mined through a precise measurement, and then utilized for the accurate determination of a mass

energy transfer coefcient in the medium of free air (Buiermann et al., 2006). This coefcient is a

signicantly important quantity for dosimetric measurements using the ion chamber with free air,

although this was estimated so far only from the calculation using data on radiation–atom interac-

tions. Moreover, W-values for electronegative gases and mixtures are being evaluated for advanced

utilization

of time projection chambers (Pushkin and Snowden-Ifft, 2009).

6.7 summary

The developments in W-value studies are described, in particular, the studies in low-energy regions

are explained in some detail in this chapter. Although the W-value is insensitive to energy and radia-

tion quality in high-energy regions, it varies considerably with decreasing energy in low-energy

regions. About 20 years ago, the photon W-value was found to show distinct variation in keV energy

regions in investigations using rare-gas proportional counters, and this nding was ascribed to the

atomic shell effect. On the basis of recent advance in synchrotron radiation researches, a variation

in photon W-values for hydrocarbon molecules was derived in the C 1s electron transition region

by means of the narrow-step energy scan. The observed oscillatory structure was well reproduced

with the model based on the valence and 1s electron transitions including Auger decays, which yield

various energies for emitted electrons. These results claried the effect of the initial photoioniza-

tion step on the variation in the energy dependence of the W-value. Absolute values for the photon

W-value of rare gas atoms were determined using the multielectrode ion chamber, which provided

results of oscillatory variations near inner-shell excitation regions. The model based on precise

atomic

shell effects has provided agreement with the measured data.

aCknowledgments

The author sincerely thanks Dr. Norio Saito of the National Metrology Institute of Japan, National

Institute of Advanced Industrial Science and Technology (NMIJ/AIST) for his close cooperation in

the study of W-values. He is indebted to the accelerator group of AIST for providing synchrotron

radiation. He would also like to thank Drs. Yuichirou Morishita and Masahiro Kato for perform-

ing measurements with the cryogenic radiometer. He appreciates the support of Prof. Kenji Ito of

Photon Factory during the writing of this chapter.

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137

Positron Annihilation in

Radiation

Chemistry

Tetsuya Hirade

Japan Atomic Energy Agency

Tokai,

Japan

and

Ibaraki

University

Mito, Japan

7.1 introduCtion

A positron is the antiparticle of an electron. It has the same mass but an opposite charge to that

of the electron. Dirac introduced an idea of the positive electron in 1930 (Dirac, 1930: 361), and,

soon after, Anderson found it, that was the positron, in 1932 during observation of radiations from

the universe, as shown in Figure 7.1 (Anderson, 1933: 491). With this discovery came into exis-

tence the study of positrons. Many techniques, such as electron paramagnetic resonance (EPR)

Contents

7.1 Introduction .......................................................................................................................... 137

7.2 Positron

Annihilation in Insulators ......................................................................................139

7.3

Positronium........................................................................................................................... 139

7.3.1 Ps

in Liquids ............................................................................................................. 139

7.3.2

in Solids ...............................................................................................................140

7.4

Experimental Techniques ..................................................................................................... 143

7.4.1 Positron

Source......................................................................................................... 144

7.4.2

Positron

Annihilation Lifetime Measurement..........................................................144

7.4.3

Doppler

Broadening Measurement........................................................................... 146

7.4.4

Age–Momentum

Correlation Measurement............................................................. 146

7.4.5

Other Techniques...................................................................................................... 147

7.5 Positronium

Formation......................................................................................................... 148

7.6

Radiation

Chemistry Studies by Positron Annihilation ....................................................... 149

7.6.1

Comparison

of the Yields of Hydrated Electrons Observed by Pulse Radiolysis.... 149

7.6.2

Comparison

of Electron Mobility Experiments ....................................................... 149

7.6.3

Electron Thermalization in Water ............................................................................ 150

7.6.4 Electric

Field Effect (Blob Model of Ps Formation)................................................. 152

7.6.5

Slow

Ps Formation in Spurs (Young-Age Broadening Effects)................................ 153

7.6.6

Formation with Trapped Electrons ...................................................................... 154

7.6.7

Reactions

of o-Ps with Spur Species ........................................................................158

7.6.8

Positronium as a Probe of Free Radicals.................................................................. 160

7.7 Positron

Annihilation on Molecules..................................................................................... 163

References...................................................................................................................................... 165

138 Charged Particle and Photon Interactions with Matter

and electron diffraction, and instruments, such as the electron microscope, are found based on

the electron. Similarly, the positron microscope (Van House and Rich, 1988: 169; Oshima et al.,

2009: 194104) and positron diffraction (Kawasuso and Okada, 1998: 2695; Fukaya et al., 2009:

193310) are found based on the positron. However, the biggest difference between the two is that

free positrons do not exist in our world. Therefore, the number of positrons that can be obtained

is quite limited. Recently, it has become possible to store a large amount of positrons and inject

them into a sample. The formation of positronium (Ps) molecules is now possible (Cassidy et al.,

2007:

062511). Ps is a bound state of a positron and an electron. It may be considered that Ps is an

isotope of the hydrogen atom.

In 1974, Mogensen proposed a Ps formation model for liquids, solids, and dense gases (Mogensen,

1974: 998). This proposal initiated the deep connection between radiation chemistry and Ps chem-

istry. The binding energy of Ps is 6.8eV, and therefore it is impossible to pick off one of the elec-

trons from the molecules, because the ionization potentials of molecules are more than 6.8eV. If

a positron is placed in liquids, solids, or gases, Ps does not form. The energetic positrons interact

with matter similarly as the energetic electrons. Then the injected positron in insulating materials

forms spurs, which thermalize in the terminal spur at the end of the track. It is called the positron

spur. The positron has a chance to capture one of the excess electrons in the positron spur to form

Ps. Once the positron and the excess electrons are trapped or solvated, Ps formation is usually very

difcult, because the lifetime of positrons in insulating materials is about 400ps. Hence, Ps forma-

tion takes place as fast as the geminate recombination of cations and free electrons, which usually

takes about 1 ps. Thus, this process provides information of very fast reactions in the spurs. There

are three methods—electron pulse radiolysis, laser ash photolysis, and the positron annihilation

method—to

study very fast reactions.

There

is another process of Ps formation at low temperatures, which is very different from

Mogensen’s model. This mechanism was claried in 1998. The details are given in Section 7.6.6.

The triplet Ps, that is, ortho-Ps (o-Ps), has the longest lifetime of 1–10ns in insulating materials, and

it can be used as a probe of reactive species, such as cation radicals and hydrated electrons. This is

explained

in Section 7.6.8.

Here,

we introduce the basic knowledge and the methods to help realize the possibilities in the

eld of radiation chemistry by using positrons. It is strongly recommended to read Mogensen’s book

(Mogensen, 1995) to understand Ps chemistry in detail. Even now, the arguments in the book have

retained

their relevance and are of interest.

Figure 7.1 A 63 million volt positron passing through a 6mm lead plate and emerging as a 23 million volt

positron.

(Reprinted from Anderson, C.D., Phys. Rev., 43, 491, 1933. With permission.)

Positron Annihilation in Radiation Chemistry 139

7.2 positron annihilation in insulators

The positron and electron annihilation can take place when these overlap each other. When they

annihilate, the energy equivalent to their total rest mass is emitted as γ-rays. These annihilation γ-rays

contain information of momenta of the electron and the positron just before the annihilation and,

hence, can be a powerful tool. The permitted number of γ-rays is governed by the conservation law of

charge

parity. The permitted number of annihilation γ-rays is even for singlet positron–

electron

pairs

and odd for triplet pairs. The annihilation probability decreases by increasing the number of annihila-

tion γ-rays, and hence almost all of the free positrons annihilate with electrons that have an anti-spin

of the positron spin, with a lifetime of about 400ps, by emitting two γ-rays. A positron and an electron

form a bound state, that is, the positronium (Ps). There are singlet and triplet Ps. The singlet Ps is called

para-Ps (p-Ps) that consists of the electron and the positron having anti-parallel spins. The triplet Ps is

called ortho-Ps, having parallel spins. The intrinsic annihilation lifetime of p-Ps is 125ps when two

γ-rays are emitted, and that of o-Ps is 142ns when three γ-rays are emitted. The intrinsic annihilation

of o-Ps has lower probability than the annihilation with one of the electrons in the surrounding mol-

ecules that has anti-spins of the positron spin. This annihilation process is called pick-off annihilation,

and the lifetime of o-Ps pick-off annihilation is usually 1–10ns. Therefore, almost all of the positron

annihilations occur mainly through free-positron annihilation, p-Ps intrinsic annihilation, and o-Ps

pick-off annihilation, giving two γ-rays for annihilation in condensed materials.

7.3 positronium

Ps is a bound state of a positron and an electron. It is considered to be a very light isotope of the

hydrogen atom (H). The reduced mass of Ps is half of the reduced mass of H. Therefore, Ps has a

Bohr

radius twice as large, 0.105

nm,

and half the ionization potential, 6.8

eV,

of H.

has negative work functions in most materials and is repelled by most materials. The electron

in Ps is repelled by the electrons in the molecules because of the Coulomb forces and the exchange

effect. The latter is a result of the Pauli principle. The space in the materials is occupied by the elec-

trons that are in the orbital of molecules. Only two electrons can occupy one orbital when they have

opposite spins, because of the Pauli principle. Therefore, they need to be in higher energy states,

rather than lled states, to penetrate into electron clouds. This causes repulsion, as the electron in Ps

needs to be in a higher energy state for penetration into other electrons. The positron is only repelled

by the positive atomic core by penetrating deep into molecules. However, the positron is kept out

of the electron clouds of the molecules because of the Coulomb attraction of the Ps electron that

is repelled by electrons of molecules, as mentioned above. This is the reason why the annihilation

probability

of free positrons is larger than the pick-off annihilation probability of o-Ps.

The

lifetime of o-Ps in condensed materials is controlled by the overlapping of the positron in Ps

and the electrons in the surrounding molecules. Therefore, it is possible to know the information of the

size of small holes in materials. As mentioned above, Ps has negative work functions in most materials

and prefers to go away from the surface. If there are holes in the material, Ps will be trapped. When the

hole size is 0.1–50nm, the lifetime of o-Ps can give information of the hole size using the Tao–Eldrup

model (Tao, 1972: 5499; Eldrup et al., 1981: 51) for smaller holes and using the extended Tao–Eldrup

model (Ito et al., 1999: 4555; Dull et al., 2001: 4657) for larger holes, as indicated in Figure 7.2.

7.3.1 ps in liQuidS

Ps is repelled by molecules, and hence it creates a bubble in liquids. The liquid pressure and surface

tension squeeze the bubble and Ps pushes the wall of the bubble. The total energy of the bubble state is

E E U r r

r p

= + +

( , ) 4

π γ

(7.1)