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

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110 Charged Particle and Photon Interactions with Matter

density, plate-to-plate distance, and so forth, W-values were elaborately estimated from the mea-

sured currents at the plates. In particular, they precisely examined the backscattering effects of inci-

dent electron beams, which resulted in the determination of accurate W-values with uncertainties

smaller than 1%. The obtained characteristics of energy dependence for some atoms and molecules

(Waibel and Grosswendt, 1978, 1983, 1991) have similar features to those found by Combecher

(1980). Further, they carried out a Monte Carlo simulation for measured W-values on the basis of

data for ionization cross sections and excitation cross sections for electron collisions with mol-

ecules. The characteristic behavior of increasing W-value with decreasing energy was well claried

by their simulation, in particular, for the W-value of methane. Figure 6.3 exhibits a comparison of

W-values for methane between experimental and calculated data (Waibel and Grosswendt, 1983).

The experimental data obtained by Waibel and Grosswendt, and by Combecher (1980) are in good

agreement with the simulation, but earlier measured data by Smith and Booz (1978) and previous

results calculated by Dayashankar (1977) are different from this calculation. According to these

studies, this behavior in the low-energy region is clearly understood by the fact that the neutral exci-

tation probability increases with decreasing electron energy in comparison with that for ionization

in collision of electrons with molecules.

By using the ion chamber technique, Samson and Haddad (1976) measured the W-value of Xe

for electrons that were ejected from Xe by the irradiation of photons of 24–90 eV from a spark-

discharge source. They reduced the acceleration of ejected electrons by the applied eld for the sake

of the ion collection technique, which utilized the cylindrical chamber having an off-axis collector

electrode. The result obtained was well reproduced with the analytic equation by Inokuti (1975),

Equation 6.1. Further, Samson and Haddad obtained the W-value for photons using the same appa-

ratus. Figure 6.4 exhibits the photon W-value for Xe as a function of energy. It has been found that

the W-value remains constant between 22 and 65eV, with a distinct increase at the 4d ionization

threshold of 67.5eV. The measured result was discussed in consideration of energy levels of Xe ionic

states and of partial photoionization cross sections for different shells.

T (eV)

W (eV)

Figure 6.3 W-values (in eV) for methane as a function of electron energy. +: Experiment (Waibel and

Grosswendt, 1983), ○: experiment (Combecher, 1980), ●: experiment (Smith and Booz, 1978), △ and solid

curve: calculation (Waibel and Grosswendt, 1983), broken curve: calculation (Dayashankar, 1977), horizontal

arrow (27.3 eV): W-value at high energies (ICRU, 1979). (Reproduced from Waibel, E. and Grosswendt, B.,

Nucl. Instrum. Method,

211, 487, 1983.)

New Directions in W-Value Studies 111

6.4 variation in energy dependenCe oF photonW-values

For

ydroCarbon

oleCules

6.4.1 introduction

On the basis of progress in electron beam techniques, studies on electron energy loss spectra pro-

vided excitation spectra of several molecules with a high resolution in the energy region of inner-

shell transitions, as well as those for rare gas atoms (Backx and van der Wiel, 1975; Hitchcock

and Brion, 1977; Key et al., 1977; King et al., 1977; Ungier and Thomas, 1984, 1985). According

to these spectra, the rst loss peak at the lowest energy is usually observed for a vacant molecular

orbital, which is the lowest unoccupied valence orbital, for example, π* orbital in a linear molecule.

The second peak comes from the transition into a Rydberg orbital in most cases, which is followed

by those into higher Rydberg orbitals and ionization continuum (Backx and van der Wiel, 1975;

Hitchcock and Brion, 1977; Key et al., 1977; King et al., 1977). Similar spectra were also measured

using monochromatized soft x-rays from synchrotron radiation sources (Eberhardt et al., 1976;

Brown et al., 1978; Hayaishi et al., 1984). Several years ago, highly resolved photoabsorption spec-

tra were obtained, which were compared with the electron energy loss spectra. Synchrotron radia-

tion studies have often shown energy resolving powers higher than those obtained using the electron

beam technique. An example of the synchrotron radiation spectra is displayed in Figure 6.5, where

photoabsorption spectrum of N

is exhibited in the N K-shell threshold region (Chen et al., 1989).

The spectrum shows a variety of peak structures corresponding to transitions of the π* orbital,

Rydberg orbitals, and ionization continua. Some peak structures have components of vibrational

excitation; in particular, π* excitation shows six or more vibrational components. Above 409.94eV

(N 1s ionization energy), some structures induced from double excitation and shape resonance are

found. Further electron emission processes were studied for many gases (Dixon et al., 1978; Rye

etal., 1978, 1980; Tamenori et al., 2004); in particular, photoelectron spectra using monochromatic

synchrotron radiation were observed for a number of atoms and molecules. Figure 6.6 shows a

photoemission spectrum of Kr with a moderate resolution at a photon energy of 410eV, where

many peaks are seen for some inner-shell photoelectrons (3s, 3p doublet, 3d, and satellites) and for

Auger electrons from the M

-shell hole states (Tamenori et al., 2004). These Auger electrons, that

is, electrons ejected through Coster–Kronig transitions, correspond to the decays of 3p

−1

states into

−1

and 3d

−1

states.

10 20 30 40 50 60 70 80 90

Photon W-value (eV)

Photon energy (eV)

Xe 4d

Figure 6.4 Photon W-value of Xe in the vacuum ultraviolet radiation region. ■: Data points. Curves con-

necting data are drawn for better presentation. The solid line in the low-energy region denotes expected values

from

physical consideration. (Modied from Samson, J.A.R. and Haddad, G.N., Radiat. Res., 66, 1, 1976.)

112 Charged Particle and Photon Interactions with Matter

As described in Section 6.3, Samson and Haddad (1976) identied a distinct variation of the

photon W-value for Xe around 70eV. This variation was ascribed to a change in the ejected electron

energy, which was caused by photoionization of the inner-shell, Xe 4d orbital. A similar variation is

expected for hydrocarbon molecules in the C K-edge region, because photoexcitation is supposed to

create several types of excited states in this energy region, yielding electrons emitted with various

energies. Recent advance in synchrotron radiation researches provides us with monochromatic soft

x-rays having continuous wavelength ranges. Therefore, we can perform studies on photon W-values

using

monochromatic soft x-rays combined with precise steps of energy scan.

Double excitations

Shape resonance

Rydberg series

×10

400 405 410

Photon energy (eV)

Absorption intensity (arb. units)

415 420

N 1s

1π

Figure 6.5 Photoabsorption spectra of N

in the soft x-ray region. Excitation of 1s electrons into the

π* orbital, and 3s, 3p, and 3d Rydberg orbitals, as well as structures by double excitation and shape resonance

are seen. Note that the ordinate scale is expanded above 404eV. (Based on Chen, C.T. et al., Phys. Rev. A, 40,

6737,

1989.)

100 150 200 250 300

0.0

2.0 × 10

4.0 × 10

6.0 × 10

8.0 × 10

10.0 × 10

Electron counts

Kinetic energy (eV)

3d satellite

3/2

1/2

Figure 6.6 Photoelectron spectra of Kr observed in the soft x-ray region. The photon energy is 410eV.

Arrows denote 3s, 3p

1/2

, 3p

3/2

, and 3d photoelectron peaks and structures by Auger electrons. (Based on

Tamenori,

Y. et al., J. Phys. B, 37, 117, 2004.)

New Directions in W-Value Studies 113

Here, we present results of photon W-values for ethylene, methane, and propane obtained using

a proportional counter, because hydrocarbon molecules used in a gas counter indicate a clear pulse

height distribution in the detection of ionizing radiation (Suzuki and Saito, 1985a,b, 1987; Saito and

Suzuki, 1986). First, the outcome for ethylene is presented and explained in detail, and then those

for

the other molecules are given.

6.4.2 MeaSureMentS and analySiS

Synchrotron radiation from the storage ring at the Advanced National Institute of Industrial Science

and Technology (to which the Electrotechnical Laboratory was reorganized in 2001) was mono-

chromatized by a plane-grating monochromator (resolving power: about 150) (Tomimasu et al.,

1983; Saito and Suzuki, 1986). The storage ring was operated in a lower-energy mode than the

normal mode for suppressing higher-order radiation. Figure 6.7 shows the experimental setup for

measurements of photon W-values for molecules (Suzuki and Saito, 1985b, 1987; Saito and Suzuki,

1986). The monochromatized photons entered a gas-ow proportional counter (Manson-4) with a

thin window (thickness: about 1500 A). Sample gases, ethylene, methane, and propane, were sup-

plied to the counter at about 5 × 10

Pa. Signals from the counter were amplied and accumulated

in a multichannel analyzer. The resultant pulse height distributions of the signals were transferred

to a personal computer. Using this computer, the pulse height distributions were analyzed to obtain

the average pulse height. An example of pulse height distribution is displayed in Figure 6.8, where

the

distribution was observed under a methane pressure of 5 × 10

Pa at a photon energy of 388eV.

The pulse height distribution can be approximately expressed by the following equation

(Breyer, 1973):

f z

z z z

( )

( / )

( ).=

⋅ −

⋅

−1

exp

Γ (6.2)

where

indicates the number of electrons amplied by the electric eld within the counter

denotes the average gas amplication factor

is the average number of the electrons initially produced by the radiation effect of a photon

Γ is the gamma function

Ring

DPS

Filter

chamber

Micro

computer

SCA

MCA

Amp

Prop.

Counter

X–Z

stage

Gas-flow

control

Gas cell

Main

chamber

PGM

Shield wall

Figure 6.7 Schematic experimental setup of measurements of photon W-values using a proportional

counter. DPS, differential pumping system; PGM, plane-grating monochromator; SCA, single-channel analyzer;

Prop.Counter, proportional counter; Amp, amplier; MCA, multichannel analyzer.

114 Charged Particle and Photon Interactions with Matter

The distributions calculated using Equation 6.2 were matched with those obtained by observation.

The

average pulse height, P, is given by

P E z f z dz z

z E

W E

x( ) ( )

( )

p a

a p

p p

= ⋅ = ⋅ =

⋅

∫

(6.3)

where

indicates the energy of a photon

denotes the W-value of photons (Suzuki and Saito, 1985a,b, 1987; Saito and Suzuki, 1986)

Using Equation 6.3, relativeW-values were obtained for photons over the energy rangeof C K-edges.

Any change in P owing to a drift in the gas pressure was canceled by measuring the P several times at

the

same photon energy in the course of the experiment. There may be photoabsorption by hydrocar-

bon

molecules in which only neutral fragments are produced, but in which no ion pair is formed. This

process should alter the W-value, although the present technique using a proportional counter cannot

count these types of processes. At present, these processes are assumed to be negligible, in consider-

ation of the results of the ionization yield of methane and other molecules in the vacuum ultraviolet

radiation region (Backx and van der Wiel, 1975).

6.4.3 reSult of ethylene

The energy dependence of the W-value is shown with solid squares for photon energies from 269 to

324eV in Figure 6.9 (Suzuki and Saito, 1987). The solid curve indicates a calculated prole based

on a model described below. The measured W-value gradually decreases from 269 to 283eV as the

photon energy increases. The W-value rises to a peak at 285eV, drops to a sharp valley at 287eV,

and

again goes up a broad peak at 290

eV.

Above a minimum at 293

eV,

the data show a near-linear

dependence on the photon energy between 293 and 301 eV. Above the latter energy, the W-value

seems

to have a slightly decreasing trend.

500

250

0 200 400

Channel number

Number of counts

600

Figure 6.8 Pulse height distribution of a proportional counter for a monochromatic soft x-ray (388eV).

Dots denote measured data, and the solid curve indicates the prole calculated with a tting technique.

(Reproduced

from Saito, N. and Suzuki, I.H., Chem. Phys., 108, 327, 1986.)

New Directions in W-Value Studies 115

It is important to consider the oscillatory variation of the W-value of ethylene in connection with

the photoexcitation of the C 1s electron. Hitchcock and Brion (1977) observed electron energy loss

spectra of ethylene for the 1s electron excitation in the energy resolution of 0.2–0.5eV. The observed

spectra show strong resonant transitions of the 1s electron to the 1b

orbital with vibrational excita-

tions at 284.68, 285.04, and 285.50eV. Ethylene is a pseudo-linear molecule, which has a π-type

orbital. This b

is often called a π* orbital. Transitions into the 3s orbital and the 3p orbital were

found to occur at 287.4 and 287.8eV, respectively. The transition into the 3s orbital is forbidden in

a spherical eld. However, this transition is allowed in a molecule although the transition strength

is weak. Transitions to higher Rydberg orbitals and to the ionized state appeared above 288.3 and

290.6eV, respectively. They further found shake-up states at 292.6 and 295.2eV. (A shake-up state

is an ionized state having an excited valence electron.) Eberhardt and coworkers (1976) observed an

electron

yield spectrum of ethylene in the same energy region by the use of monochromatized syn-

chrotron

radiation. The same transitions were identied although the resolution was lower andthe

observed

values deviated slightly (0.3–0.7

eV).

6.4.4 SiMple Model for explanation of variation in W-value

A comparison between the inner-shell excited states and the energy dependence of the W-value

provides us with a model for interpretation as follows. For simplicity of explanation, energy regions

are divided into seven parts. In each energy region, only one photoionization process is considered,

and others are neglected owing to very small probability. Figure 6.10 illustrates a change in electron

conguration during subsequent electron emission following initial photoabsorption, together with

the nal charge state of the present molecule. Table 6.2 lists energy values necessary for the calcu-

lation of the W-value on the basis of the present model. These energies have been estimated from

available data in the literature, for example, Auger electron spectra and photoelectron spectra (Rye

al., 1978; Liegener, 1985; Kimura et al., 1981; Suzuki and Saito, 1987).

(i) Below 284.7 eV: Only a valence electron is ejected by photoabsorption, because the pho-

ton cannot excite an inner-shell electron. The average energy of this ejected electron is

− E

, where E

is the average binding energy of the valence electrons. Ethylene has six

orbitals for valence electrons, which are 1b

, 1b

, 3a

, 1b

, 2b

, and 2a

(Dixon et al., 1978;

270

0.96

1.0

Relative W-value

1.04

1.08

280 290

Photon energy (eV)

300 310

320

Figure 6.9 Photon W-value for C

as a function of soft x-ray energy. Solid squares indicate measured

data. The solid curve and a broken line denote the calculated prole based on the model explained in Section 6.4.4.

(Reproduced

from Suzuki, I.H. and Saito, N., Bull. Chem. Soc. Jpn., 60, 2989, 1987.)

116 Charged Particle and Photon Interactions with Matter

table 6.2

list

of e

nergy

alues

ecessary

for Calculation

the p

hoton

W-

value

of e

thylene

in the

odel

at s

ection

6.4.4 (in e

W-value for sufciently high energy

radiation

W 25.8

Average

energy of sub-ionization

electron

for an electron with an

energy

for E ≥ 200

for E ≤ 33

First

ionization energy E

10.5

Average

of ionization energy for

valence

electron

16.1

Ionization

energy of the K-shell E

290.6

Average

energy of

Auger

electron E

245.8

Average

energy of de-excitation

electron

from the (1s)

−1

(π*)

state

Aπ

255

Average

energy of de-excitation

electron

from the (1s)

−1

(R)

state

255

Average

energy gain of

Auger

electron

in a post-collision

interaction

− 288

Note: π* and R indicate 1b

and Rydberg orbitals, respectively.

denotes photon energy.

Case

Charge of

residual ion

Final

conﬁguration

Initial

conﬁguration

Energy

range

< 284.7

(a)

285.1 ≤ E

< 287.4

π*

x x

(i) and (iii) (vi) and (vii)(ii) (iv) (v)

21 1

(b) (c) (d) (e)

284.7 ≤ E

< 285.1

287.4 ≤ E

< 290.6

290.6 ≤ E

< 291.5 291.5 ≤ E

Figure 6.10 Change in electron conguration during electron emission and nal charge state of the mol-

ecule. K, V, R, and π* indicate the K-shell, the valence orbitals, the Rydberg orbitals, and the π* orbital,

respectively.

x: occupation by an electron,

○: hole in the valence orbital or the K-shell.

New Directions in W-Value Studies 117

Kimuraet al., 1981). The value of E

is assumed to be 16.1eV. The ejected photoelectrons ion-

ize ambient molecules and produce a number of ion pairs. On the other hand, the W-value of

low-energy electrons (W

) can be approximately given by the following equation, as indicated

in Section 6.2 (Inokuti, 1975; Samson and Haddad, 1976; Combecher, 1980):

W E

E W

E U

( )

⋅

−

(6.4)

where

W denotes the W-value for radiation with a sufciently high energy for ethylene (25.8eV)

(ICRU,

1979)

U indicates the average energy of sub-ionization electrons

is the energy of an emitted electron

The sub-ionization electrons are the electrons that do not contribute to ionization in a sys-

tem receiving irradiation. In the present instance, the average number of ion pairs, N

, is

given

E U

= =

−( )

. (6.5)

Using

Equations 6.4 and 6.5, the photon W-value is expressed by the following equation:

W E

E W

E W E U

p p

p v 1

( )

( ) ( )

⋅

+ − −1

(6.6)

where U

is assumed to be 22eV from the data for the W-value of low-energy electrons

(Combecher, 1980). Multiple photoionization of the valence electrons is assumed to occur

only

at negligibly low probability at present.

(ii) Between 284.7 and 285.1

eV: The 1s electrons can be excited to the π* orbital (1b

), and

a hole is formed in the C K-shell. After this excitation, an Auger transition is supposed to

occur, because uorescence yield is extremely low in a light element. A variety of Auger

transitions have been observed in ethylene (Rye et al., 1978; Liegener, 1985). The average

energy of Auger electrons, E

, is estimated here to be 245.8eV, according to the spectrum

by Rye et al. (1978). However, the average Auger electron energy in the present instance

is supposed to be somewhat higher than 245.8eV owing to the existence of that electron

in the π* orbital. This average energy, E

Aπ

, is assumed to be 255eV, by analogy from a

resonance-type Auger electron spectrum of CO (Ungier and Thomas, 1984, 1985). The

W-value

is expressed by

W E

E W

E W U

p p

A 1

( )

( ) ( )

⋅

+ −1

(6.7)

When Equation 6.7 is compared with Equation 6.6, E

Aπ

(255eV) is lower than E

− E

(e.g.,270.9eV

for the photon with an energy of 287

eV).

This fact implies that the W-value

at 284.7eV becomes higher than that at 287eV. In the present model, it is assumed that the

photoabsorption probability involving valence electrons can be negligibly low in this pho-

ton energy region on account of the spectra of the inner-shell excitation (Eberhardt et al.,

1976; Hitchcock and Brion, 1977; Brown et al., 1978; Henke et al., 1993). This assumption

also applied to the energy region above 287.4

(case iv to case vii).

118 Charged Particle and Photon Interactions with Matter

(iii) Between 285.1 and 287.4 eV: Photons can excite only valence electrons, because there is

no inner-shell excited state in this region. Ejected photoelectrons ionize ambient molecules

and

produce a number of ion pairs. W

is expressed by Equation 6.6.

(iv) Between 287.4 and 290.6

eV: Photons can excite inner-shell electrons to the Rydberg orbit-

als, and then the formed inner-hole is lled with a valence electron through the subsequent

Auger transition. The average energy of the Auger electrons, E

, is assumed to be 255eV.

(v) Between 290.6 and 291.5

eV: Inner-shell electrons can be ejected from the molecule by

photons,

but these ejected photoelectrons leave slowly. In the case of CO, the K-shell pho-

toelectron

with low energy is retrapped by the molecular ion when a second electron with

higher energy is ejected by an Auger transition (post-collision interaction [PCI]) (Key

etal., 1977; Hayaishi et al., 1984). Since there has been no detailed study on these mol-

ecules, the slow photoelectron in the present case is assumed to be retrapped at the instant

of the Auger transition. The Auger electron obtains a slightly higher energy owing to the

existence of the slow photoelectron than the normal Auger electron. This energy gain of

the Auger electron is equal to the energy loss of the trapped electron. The average energy

of the Auger electron is assumed here to be 245.8 + α eV (α = E

− 288eV), because of no

available data in molecules. This PCI is tentatively assumed to occur between 290.6 and

291.5eV, in consideration of the energy giving a minimum W-value (293eV) and of the

photon

energy resolution.

(vi) Between 291.5 and 301.1

eV: The inner-shell electrons can be ionized and can promptly

escape from the molecular eld. This photoelectron ejection is followed by a normal Auger

transition. The photoelectron has an energy of E

− 290.6eV. However, this electron cannot

ionize other ambient molecules because the electron energy is lower than the rst ioniza-

tion energy of the valence electron (E

= 10.5eV). The Auger electron (E

) has an average

energy

of 245.8

eV.

(vii) Above 301.1

eV: The photoelectron released from the inner shell has an energy higher

than the rst ionization energy of ethylene. This electron and the Auger electron produced

subsequently can ionize ambient molecules. The W-value is expressed by the following

equation:

W E

N N

E W

E E W E U U

p p

e1 e2

p A K 1 2

( )

( ) ( )

+ +

⋅

+ + − − −2 2

(6.8)

where U

denotes the average energy of the sub-ionization electrons for the electron with

kinetic energy between 11 and 33 eV. U

is assumed to be 11eV on the basis of the study by

Combecher

(1980).

using the present model, the relative W-value has been calculated and shown with the solid

curve in Figure 6.9. The resolving power of the monochromator was not included in this calcula-

tion. Energy dependence of the calculated W-value is in agreement with the experimental results.

Therefore,

the present model is essentially correct.

There

is a slight discrepancy between the experimental data and the calculated result at a few

energies. The discrepancy at 286eV is ascribed to the low resolving power of the present monochro-

mator, while that between 291 and 293eV is presumed to originate from two reasons, other than low

resolving power. First, although the energy of the electron may be lowered through a post-collision

interaction below 291.5eV, there is a possibility that some fraction of slow photoelectrons are not

retrapped by the molecular ion. If this is the case, the nal conguration is that having two holes in

the valence orbital. The calculated W-value becomes lower than that shown in Figure 6.9 between

290.6 and 291.5eV. Second, slightly distorted pulse height distributions in the proportional counter

New Directions in W-Value Studies 119

around 291eV have been observed. The width of the distribution was broader than those at other

energies. This phenomenon is supposed to be brought about by a contamination of the used grating

in the soft x-ray monochromator, which resulted in a decrease of output intensity near the C K-edge.

This should cause the effective resolving power to be lower. From the minimum at 293eV (not at

290.6eV), it can be said that the post-collision interaction takes place just above the C K-edge.

However, it is impossible at present to estimate the size of the energy region where it occurs. The

broken line between 290.6 and 291.5eV in Figure 6.9 shows the calculated result in case of no

occurrence

of the post-collision interaction.

The

reason why the experimental data are slightly lower than the calculated curve near 280eV

is not clear at present. The photoabsorption cross section near 280eV is very low owing to no exci-

tation of inner-shell electrons. The electron cloud induced by photoabsorption is distributed more

homogeneously in the proportional counter near 280eV than other energies. This fact may have a

small effect on the average pulse height distribution through a possible change in the gas amplica-

tion

factor.

The

shake-up states were reported to exist at 292.6 and 295.2eV in the literature (Hitchcock and

Brion, 1977). In contrast to the transition to the π* orbital, the transition probability to these states

was considerably lower than to the normal continuum state. Thus, this transition was not expected

to have an appreciable effect on the W-value. The experimental W-value does not show a change at

the

energies in Figure 6.9 within experimental uncertainty.

6.4.5 Methane and propane

Methane is usually used as a counter gas for the measurement of ionizing radiation. Since the

photoabsorption spectrum of methane shows a ne structure near the C K-edge due to transitions

of C 1s electrons (Eberhardt et al., 1976; Brown et al., 1978), the W-value of methane may also

have a ne structure related to these transitions.

Figure 6.11 shows the relative W-value of methane for photon energies between 240 and 400 eV

(Saito and Suzuki, 1986). Open and solid circles denote the data obtained by using Al and the

copolymer of vinyl chloride and vinyl acetate (VYNS) windows, respectively. The W-value gradually

250

0.95

Relative W-value

1.05

300

Photon energy (eV)

350 400

Figure 6.11 Photon W-value for CH

as a function of soft x-ray energy. Solid and open circles indicate

measured data using the VYNS window and the Al window, respectively. The solid curve denotes the cal-

culated prole based on the model explained in Section 6.4.5. (Reproduced from Saito, N. and Suzuki, I.H.,

Chem. Phys.,

108, 327, 1986.)