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

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20 Charged Particle and Photon Interactions with Matter

2. NH

a. Balmer-α, -β, -γ, -δ, and -ε

b. NH(A

→ X

−

), NH(c

Π → a

Δ), and NH(c

Π → b

)

3. H

a. Balmer-α,

-β, -γ, -δ, -ε, -ζ, and -η

b. OH(A

→ X

)

c. OH

→ X

−

)

d. H

(Ã

(3a

)

−1

→ X

(1b

)

−1

)

As an example of the uorescence cross-section curves that we measured, that is, the absolute

values of the cross sections for the emission of the Balmer-β uorescence, H(n = 4 → n′ = 2),

in the photoexcitation of CH

as a function of incident photon energy (Kato et al., 2002: 4383)

are shown in Figure 2.7 together with experimental (Göthe et al., 1991: 2536) and theoretical

(Cederbaum et al., 1978: 1591) photoelectron spectra. In Figure 2.7a, the left and right vertical axes

represent the cross section and oscillator strength distribution for the emission of the Balmer-β

uorescence, respectively. The peaks around 22 and 29eV in Figure 2.7a are clearly attributed to

250 300 350 400 450 500

19.0 eV

28.4 eV

Intensity (arb. units) Intensity (arb. units)

n = 456789

Series limits

Fluorescence wavelength (nm)(b)

(a)

n = 4567

δε

η γ

δε

η γ β

)

Series limits

OH(A

, Δν = 0)

Balmer series, H(n n

= 2)

Balmer series, H(

n n

= 2)

)

OH(A

, Δν = 0)

–

, 0 0)

Figure 2.6 Fluorescence spectra in the photoexcitation of H

O measured with a spectral resolution of

2.9nm. The incident photon energies were (a) 19.0eV and (b) 28.4eV. The uorescence intensities were nor-

malized for the incident photon ux, the target gas pressure (≈1.6Pa), and the accumulation time, and then the

normalized intensities were plotted against the uorescence wavelength without correcting for the sensitivity

of a whole system. This correction was, of course, carried out to obtain the absolute values of the cross section

for the emission of each uorescence, as was described in detail by Kato et al. (2002: 4383). (From Kato, M.

al., J. Phys. B, 37, 3127, 2004. With permission.)

Oscillator Strength Distribution of Molecules in the Gas Phase 21

the superexcited states of CH

since they are above the (1t

)

−1

ionic state of CH

. It is still difcult

to substantiate these superexcited states because there are no theoretical investigations as far as we

know. Thus, let us rely on the knowledge of the ionic states of CH

that were investigated much

better than the superexcited states of CH

by means of photoelectron spectroscopy, as shown in

Figure 2.7b. There exist four double-hole one-electron states above the single-hole (2a

)

−1

state

around 23.0eV, that is, the (1t

)

−2

(2t

) state around 29.2 eV, the (1t

)

−2

(3a

) state around 32.1 eV,

the (2a

)

−1

(1t

)

−1

(2t

) state around 38.5 eV, and the (2a

)

−2

(3a

) state around 43.3eV, the highest of

which is out of range in Figure 2.7a. The neutral superexcited molecule is considered a molecule

in which one electron is bound on the ion as an ion-core. Let us substantiate the superexcited

states around 22 and 29eV along this line; it hence follows that these superexcited states seem

10 15 20 25 30 35 40

Energy (eV)

Cross section (arb. units)

Cross section (10

–20

)

(2a

)

–1

(1t

)

–2

(2t

)

(1t

)

–2

(3a

)

(1t

)

–1

(1a

)

(2a

)

(1t

)

0.5

(a)

(b)

1.5

0.5

(df/dE)

Bal

(10

–4

–1

)

H(4)+CH

(X)

H(4)+CH

(X)+e

–

H(4)+ C (2p

P)+ 3H(1)

H(n =4

=2)

(×5)

(2a

)

–1

)

Doubly excited

D2 states

H(4)+C

(2p,

P)+ 3H(1) + e

–

(2a

)

–1

(1t

)

–1

(2t

)

Figure 2.7 (a) Cross sections (left axis) and oscillator strength distributions (right axis) for the emission

of the Balmer-β uorescence, H(n = 4 → n′ = 2), in the photoexcitation of CH

as a function of incident

photon energy (Kato et al., 2002: 4383). The dissociation limits for the formation of H(n = 4) are indicated

by the short vertical bars. (b) Experimental and theoretical photoelectron spectra: The photoelectron spec-

trum of CH

taken at a photon energy of 65 eV and an angle of 90° with respect to the electric vector of the

incident polarized light (solid curve) (Göthe et al., 1991: 2536) and the corresponding spectrum calculated

by Cederbaum et al. (vertical bars) (Cederbaum et al., 1978: 1591). The horizontal axes indicate the incident

photon energy in (a) and the binding energy in (b). The ground electronic state of CH

in T

symmetry is

shown in the upper part. (From Kouchi, N., Measurements of the uorescence cross sections in the photo-

excitation of CH

, NH

and H

O in the vacuum ultraviolet range, in Atomic and Molecular Data and Their

Applications: Joint Meeting of 14th International Toki Conference on Plasma Physics and Controlled

Nuclear Fusion (ITC14); and 4th International Conference on Atomic and Molecular Data and Their

Applications (ICAMDATA2004), AIP Conference Proceedings, T. Kato, H. Funaba, and D. Kato (eds.), Vol.

771, 199–208, 2005. With

permission.)

22 Charged Particle and Photon Interactions with Matter

to be built on the single-hole (2a

)

−1

state around 23.0eV and (1t

)

−2

(3a

) state around 32.1eV,

respectively. Superexcited states around 22eV are thus singly inner-valence excited states with

the electron conguration of (2a

)

−1

(mo), and those around 29eV are doubly excited states with the

electron conguration of (1t

)

−2

(3a

)(mo′), where mo and mo′ refer to molecular orbitals. The singly

inner-valence excited (2a

)

−1

(mo) states around 22 eV were also observed by measuring the excita-

tion spectra for the formation of H

−

(Mitsuke et al., 1991: 6003; Mitsuke et al., 1993: 6642) and

threshold photoelectrons (Dutuit et al., 1990: 223; Furuya et al., 1994: 2720), and the excitation

spectra for the emission of undispersed uorescence (Sorensen et al., 1995: 554). Considering their

results, the singly inner-valence excited states around 22eV were assigned the (2a

)

−1

(n″pt

)

Rydberg states (n″= 3 and 4). On the other hand, the doubly excited (1t

)

−2

(3a

)(mo′) states around

29eV have not been understood well and were labeled D2. The doubly excited states labeled D1

and D3 were observed in the cross-section curves for the emission of CH(A, B → X) uorescences

in the photoexcitation of CH

. Interestingly, the doubly excited D2 states are not responsible for

the emission of CH(A, B → X) uorescences. More recently, the doubly excited D4 states with the

electron conguration of (2a

)

−2

(3a

)(mo″) were found in the cross-section curve for the emission

of the Lyman-α uorescence in the photoexcitation of CH

(Fukuzawa et al., 2005: 565). The 2a

orbital in the D4 states is fully unoccupied, and hence they are hollow molecular states. This was

the rst report of nding hollow states of molecules.

The most remarkable feature of Figure 2.7a is that the cross sections originating from doubly

excited D2 states seem to be much larger than those expected within the independent electron

model, where double photoexcitation is much weaker than single photoexcitation since the electric

dipole moment,

∑

s s

, in Equation 2.2, is a sum of single-electron coordinates. It is more convenient

to discuss this interesting feature in terms of oscillator strength. The integration of each peak in

the cross-section curve in Figure 2.7a over the range of incident photon energy gives the oscillator

strength for the emission of the Balmer-β uorescence originating from each superexcited state, as

the following equation:

σ π α

E a R

( )













. (2.33)

Equation 2.33 is easily derived from Equations 2.14, 2.16, and 2.17. Channel q in Figure 2.7a is

the emission of the Balmer-β uorescence, and thus (df/dE)

is written as (df/dE)

Bal

, the scale of

which is shown on the right vertical axis of Figure 2.7a following Equation 2.33. The oscillator

strength, f

Bal

, for the emission of the Balmer-β uorescence in CH

originating from the singly

inner-valence excited (2a

)

−1

(n″pt

)

states (n″ = 3 and 4) and doubly excited D2 states were

obtained as follows:

f n

Bal

((2a ) ( pt )) 1.7 10 ,

− −

′′

= ×

(2.34)

Bal

(D2) 3.4 10 .= ×

−4

(2.35)

Equations 2.34 and 2.35 are indicative of the breakdown of the independent electron model, which

is probably due to a mixing between the doubly excited D2 states and nearby singly inner-valence

excited (2a

)

−1

(n″pt

)

states, that is, due to the electron correlation. We note that the oscilla-

tor strength for the emission of the Balmer-β uorescence is given by the product of the oscillator

strength for excitation to the precursor superexcited state and the branching ratio of the formation

of H(n = 4) fragment atoms. This point was discussed in detail by Kato et al. (2002: 4383), and

the above conclusion, that is, the breakdown of the independent electron model, was drawn. The

experimental photoelectron spectrum in Figure 2.7b also shows the breakdown of the independent

electron model: the single-hole (2a

)

−1

main peak due to one-electron ionization is accompanied

Oscillator Strength Distribution of Molecules in the Gas Phase 23

by the satellite peaks due to one-electron ionization and one-electron excitation. The degree of

the breakdown in the photoexcitation process (Figure 2.7a) is much larger than in the photoioniza-

tion process (Figure 2.7b) since the “satellite” peak around 29eV is stronger than the “main” peak

around

in Figure 2.7a.

The

cross sections for the emission of the Balmer-β uorescence, H(n = 4 → n′ = 2), in the

photoexcitation of NH

and H

O as a function of incident photon energy are shown in Figure 2.8

10 15 20 25 30 35 40

Satellite

(2a

)

–1

)

Satellite

×5

(1b

)

–1

(mo)

(2a

)

–1

(mo)

H(4)+OH(X)

H(4)+NH

(X)

H(4)+CH

(X)

H(4)+NH

(X)+e

–

H(4)+CH

(X)+e

–

(1b

)

–1

(3a

)

–1

(1t

)

–1

(2a

)

–1

(2a

)

–1

(1e)

–1

(3a

)

–1

(1b

)

–1

(2a

)

–1

H(4)+OH

(X)+e

–

Satellite

H(n =4 n

=2)

Balmer-β

0.5

1.5

0.5

Satellite

Photon energy (eV)

(df/dE)

Bal

(10

–4

–1

)

Cross section (10

–20

)

(2a

)

–1

(mo)

H(n =4 n

=2)

H(n=4

=2)

Figure 2.8 Cross sections (left axis) and oscillator strength distributions (right axis) for the emis-

sion of the Balmer-β uorescence, H(n = 4 → n′ = 2), in the photoexcitation of CH

(Kato et al., 2002:

4383), NH

(Kato et al., 2003: 3541), and H

O (Kato et al., 2004: 3127) as a function of incident photon

energy. The vertical ionization potentials for the single-hole states and double-hole one-electron states (sat-

ellites) are indicated together with the dissociation limits for the formation of H(n = 4). D1 and D2 refer

to doubly excited states and “mo” refers to a molecular orbital.

CH X A a a t

: ( ) ( ) ( )



1 1

1 2 1 in T

symme-

try (Herzberg, 1991: 348),

NH X A a a e a

1 1

1 2 1 3: ( ) ( ) ( ) ( )



in C

symmetry (Herzberg, 1991: 609), and

H O X A a a b a b

1 1

1 2 1 3 1: ( ) ( ) ( ) ( ) ( )



in C

symmetry (Herzberg, 1991: 585). (From Kato, M. et al.,

J.Phys. B,

37, 3127, 2004. With permission.)

24 Charged Particle and Photon Interactions with Matter

together with those in CH

. The right vertical axis represents the oscillator strength distributions

for the emission of the Balmer-β uorescence. The cross-section curves of NH

and H

O were

analyzed in the same way as CH

, and the doubly excited states labeled D1 and D2 as well as the

singly inner-valence excited (2a

)

−1

(n″pt

) or (2a

)

−1

(mo) states were found. The contribution from a

superexcited state is approximated by a Gaussian function according to the multidimensional reec-

tion approximation (Schinke, 1993: 109–120), and the result of the tting is shown by the dashed

lines in Figure 2.8. Such a procedure was needed for NH

and H

O since peaks are not separated

well. The tting was also done for CH

. The peak due to the singly outer-valence excited (1b

)

−1

(mo)

states is seen only in the cross-section curve of H

O because of energetic reasons (see the vertical

ionization potentials indicated by vertical bars with hatches, and dissociation limits for the forma-

tion of H(n = 4) indicated by vertical bars). We note that the superexcited states in Figure 2.8 were

observed by measuring cross-section curves or oscillator strength distributions free from ionization,

and that doubly excited states were rst found by Kato et al. (2002: 4383; 2003: 3541; 2004: 3127).

Interestingly, as shown in this gure, energies of the singly inner-valence excited (2a

)

−1

(n″pt

) or

(2a

)

−1

(mo) states become higher on going from CH

to H

O, while those of the doubly excited D2

states do not change quite so much. Figure 2.8 also seems indicative of the breakdown of theinde-

pendent electron model. This is well illustrated in Figure 2.9, where oscillator strengths for the

emission of Balmer uorescences, H(n → n′ = 2), in CH

(Kato et al., 2002: 4383), NH

(Kato

etal., 2003: 3541), and H

O (Kato et al., 2004: 3127) are plotted against n on logarithmic scales for

both axes. The independent electron model seems violated in the energy range near the ionization

potential of the inner-valence 2a

electron in CH

, NH

, and H

O. In particular, the result of CH

Figure

2.9, that is,

f f n

Bal Bal

(D2) ((2a ) ( pt )),

1 2

′′

−

(2.36)

is remarkable. We again note that f f n

Bal Bal

(D2) a pt (( ) ( ))2

−

′′

is expected within the indepen-

dent electron model. There seems to be a tendency that the degree of breakdown of the independent

electron

model becomes lower on going from CH

to H

4 5 6 7 8 9

ONH

4 5 6 7 8 9

–5

–4

–3

Oscillator strength

4 5 6 7 8 9

(2a

)

–1

(mo)

(1b

)

–1

(mo)

(2a

)

–1

)

(2a

)

–

(mo)

Figure 2.9 Oscillator strengths for the emission of the Balmer uorescences, H(n → n′ = 2), in CH

(Kato

et al., 2002: 4383), NH

(Kato et al., 2003: 3541), and H

O (Kato et al., 2004: 3127) plotted against the prin-

cipal quantum number of the upper level of the hydrogen atom, n, on logarithmic scales for both axes. Open

diamonds: (1b

)

−1

(mo), open triangles: (2a

)

−1

(mo) or (2a

)

−1

(n″pt

), open squares: D1, and open circles: D2. D1

and D2 refer to doubly excited states and “mo” refers to a molecular orbital. (From Kato, M. et al., J. Phys. B,

37,

3127, 2004. With permission.)

Oscillator Strength Distribution of Molecules in the Gas Phase 25

2.5 ConClusion

The oscillator strength distribution for photoabsorption (df/dE) or the photoabsorption cross sec-

tion (σ) as a function of incident photon energy gives the basic feature of the interaction of photons,

as discussed in Section 2.1 and by Kouchi and Hatano (2004: 105–120). However, the peaks due

to superexcited states, in particular, singly inner-valence excited and multiply excited states, are

not noticeable in the df/dE or the σ curve because of a large contribution of ionization. The key

to observing superexcited states is thus measuring the “partial” oscillator strength distribution or

cross section free from ionization as a function of incident photon energy. The typical ioniza-

tion-free process is a neutral dissociation following the superexcitation, and thus we can observe the

superexcited states by measuring the oscillator strength distribution or cross section for the emission

of uorescence from neutral fragments as a function of incident photon energy. The results of such

measurements carried out for 10-electron molecules, that is, CH

, NH

, and H

O, are presented as

an example. We stress that it is signicant to measure absolute values of the oscillator strength dis-

tribution or cross section for a detailed and quantitative discussion. The singly inner-valence excited

and doubly excited states were clearly observed, which shows that the above-mentioned method is a

powerful tool. A strong indication of the breakdown of the independent electron model was found.

The observed peaks are not classied into main peaks due to singly excited states and into satellite

peaks due to doubly excited states. The effect of electron correlation has to be considered in a proper

way

to describe the dynamics of superexcited states as well as energy eigenvalues.

aCknowledgments

The authorswish to thank Drs. Masahiro Kato,Kosei Kameta,and MakotoMurata, andProf. Yoshihiko

Hatano for their excellent contribution to the investigations described in Section 2.4. The successful

results

presented in Section 2.4 are due to the high stability of the synchrotron radiation at the Photon

Factory, Institute of Materials Structure Science, KEK, Tsukuba, Japan, and the negligibly low inten-

sity of the higher-order component mixed in incident light at the BL-20A of the Photon Factory.

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Electron Collisions with

Molecules

in the Gas Phase

Hiroshi Tanaka

Sophia University

Tokyo,

Japan

Yukikazu Itikawa

Institute of Space and Astronautical Science

Sagamihara,

Japan

Contents

3.1 Introduction ............................................................................................................................28

3.2 Fundamental

Aspects of Collision Processes.........................................................................29

3.2.1

Source

of Secondary Electrons...................................................................................29

3.2.2

Collision

Cross Section and Related Quantities.........................................................29

3.2.3

Theory

and Its Role ....................................................................................................32

3.3

Recent Advances in Low-Energy Electron Collisions with Molecules.................................. 33

3.3.1 Overview

of the Cross Sections for Electron Collisions with Molecules...................33

3.3.2

Measurements

by Electron-Beam Attenuation and Transport Methods .................... 35

3.3.2.1

Total Scattering Cross Section—An Upper Bound of Cross Section ...................35

3.3.2.2 The

Swarm Method to Determine a Cross-Section Set...............................37

3.3.3

Crossed-Beam Methods for the Measurement of Cross Section................................38

3.3.3.1 Crossed-Beam

Methods and the Measurement of DCS ..............................38

3.3.3.2

Measurements of DCS over the Full Range of Scattering Angles................. 40

3.3.3.3 Electron

Spectroscopy at High Resolution .................................................. 41

3.3.4

Cross

Sections for the Production of the Secondary Species..................................... 47

3.3.4.1

Ionization Cross Section .............................................................................. 47

3.3.4.2 Dissociation

to Produce Neutral Fragments ................................................49

3.3.4.3

Negative-Ion

Production.............................................................................. 51

3.3.5

Collision

Processes Involving Vibrationally Excited Molecules................................ 52

3.3.6

Complete

Collision Dynamics in (e, 2e) Experiments for H

O.................................. 55

3.4 Applications

of Cross-Section Data and Databases ...............................................................57

3.4.1

Energy

Deposition Model Based on Collision Cross Sections................................... 57

3.4.2

Electron

Transport in High-Pressure Xe Doped with CH

..........................................58

3.4.3 Databases....................................................................................................................59

3.5 Conclusions.............................................................................................................................60

Acknowledgments............................................................................................................................60

References........................................................................................................................................60

28 Charged Particle and Photon Interactions with Matter

3.1 introduCtion

Radiation interaction with matter is a subject of radiation science (i.e., radiation physics, radiation

chemistry, and radiation biology). This subject is roughly divided into two parts. The rst is the

fate of incident radiation, or, more specically, the amount of energy deposited in matter (the linear

energy transfer (LET) or stopping power). The second is the change of matter due to the absorption

of radiation energy. Both aspects of radiation–matter interaction are understood microscopically

in terms of collisions among the radiation particle, the medium molecules, and the products of the

interaction itself. Thus, knowledge of the relevant atomic collision processes is an essential ingredi-

ent of radiation science. As a part of this knowledge, this chapter provides a general picture of the

collisions between electrons and molecules. The roles that these electron–molecule collisions play in

radiation–matter interaction are described in other chapters.

Now, we consider ionizing radiation (i.e., fast charged particles and high-energy photons). In the

interaction of ionizing radiation with matter, the most dominant microscopic process that occurs is

the ionization of medium molecules (production of ions and free electrons). If the ejected electron

has a large enough energy, it can ionize the medium molecules further. The free electrons thus pro-

duced are called “secondary electrons.” Many of the chemical or biological effects of radiation are

triggered by the action of these secondary electrons. For example, a part of the radiation damage to

DNA (called the direct damage) is due to the direct interaction of secondary electrons with the DNA

molecule. As is shown in Section 3.2.1, most of the secondary electrons have energies less than

100 eV. These electrons are often called low-energy electrons, compared with the fast electrons in

the primary radiation. Section 3.3 summarizes the recent advances in the study of the collisions of

these low-energy electrons with molecules.

The behavior of the secondary (and the primary, if any) electron is studied in two different ways:

calculation of the degradation spectrum and the Monte Carlo simulation. The distribution function of

the electron energy satises a kinetic equation. On the basis of the kinetic theory, Spencer and Fano

derived an equation governing the degradation process of the electron energy spectrum (see the review

by Kimura etal., 1993). Once the spectrum is obtained, one can calculate the yield of a particular spe-

cies produced during radiation interaction with matter. Another approach is the Monte Carlo simula-

tion (see Section 3.4). It numerically traces all the trajectories of a number of representative electrons

in matter. It reveals the three-dimensional structure of the radiation track, leading to the understanding

of biochemical and biological effects of radiation (Nikjoo etal., 2006). Both these methods require the

information of collision processes between electrons and matter molecules (i.e., cross-section data).

Particularly, in the Monte Carlo method, this information is necessary on the outgoing direction of the

electron after collision (i.e., the differential cross section [DCS]).

To advance on with radiation science, it is essential to have a reliable set of cross-section data for

the collision processes involved. According to Inokuti, for these cross-section data to be applicable

to any practical problem, they must fulll the trinity requirement, that is, the data should be correct,

absolute, and comprehensive. Here, the term “comprehensive” means that the data must cover a wide

enough range of variables (e.g., incident energy and scattering angle). On the contrary, data are often

available only over a limited range of variables. There have been several attempts to compile a reliable

database of the cross section for electron–molecule collisions. Some examples are given in Section 3.4.

Some specic processes of electron–molecule collisions are of special importance in the interac-

tion of radiation with matter. Recently, collisions of low-energy electrons with biological molecules

are being extensively studied. The dissociation of molecules via collision with electrons of very low

energies (≲10eV) has been highlighted in relation to radiation damage of DNA. This topic is briey

discussed

in Section 3.3.

Electron–molecule

collisions play fundamental roles in various application elds. For exam-

ple, they are important in the study of the upper atmosphere (ionosphere) of the Earth and other

planets. The understanding of low-temperature plasmas (e.g., those used for plasma processing)

is based on the knowledge of electron–molecule collisions. This chapter serves also as a guide

Electron Collisions with Molecules in the Gas Phase 29

toelectron–molecule collisions in these fields. More details of the electron–molecule colli-

sion data and their applications are given in a book by Itikawa (2007). Finally, it should be

pointed out that the discussion in this chapter is restricted to the collision processes in the gas

phase. Of course, collision processes in the liquid phase (or in other condensed phases) are

also important in the study of radiation interaction with matter. These topics are treated in

other chapters.

3.2 Fundamental aspeCts oF Collision proCesses

3.2.1 Source of Secondary electronS

The interaction of a charged particle with a molecule can be broadly divided into two categories:

distant (or soft) collision and close (or hard) collision. When the charged particle is located far

from the target molecule, it exerts an electromagnetic force over the entire molecule, and the

interaction resembles the photoabsorption of the molecule. On the other hand, when the incident

particle comes close to the target, a knock-on collision occurs between the particle and the bound

electron in the molecule. In this case, the interaction can be described by a binary-encounter

model. Ionization cross sections are approximately constructed by combining the models in

these two categories (Kim and Rudd, 1994). More details of the ionization process are given by

Toburen (2004).

A secondary electron is characterized by two parameters: its kinetic energy and its moving

direction with respect to the beam of incident particles. The distribution of energy and angles of

the electron ejected after an ionizing collision are specied by the so-called doubly differential

cross section (DDCS) of ionization. When we integrate the DDCS over the angles, we obtain the

energy distribution of the ejected electron (called the singly differential cross section, SDCS). One

can easily note that the integration of the SDCS over the energy of the ejected electron leads to

the ionization cross section.

As an example, Figure 3.1 (Ohsawa etal., 2005) shows the DDCS for the ionization of water

O) vapor by the impact of alpha particles. Figure 3.2 (Bolorizadeh and Rudd, 1986) gives the

SDCS for the ionization of H

O by electron collisions. Both gures show that the energy distribu-

tion of the secondary electron has a peak at around zero energy. In other words, the energy of most

of the secondary electrons is less than about 100eV. These gures show the spectra of the rst gen-

eration

of secondary electrons. Electrons with impact energy above the ionization potential of H

(12.6eV) can ionize H

O molecules further. The resulting free electrons are the second generation

of secondary electrons. Thus, the mean energy of the secondary electron beam is lower than that of

the

spectra shown in the gures.

Collisions

of fast photons with molecules also generate free electrons. When the photon energy

is lower than about 10keV, these electrons are ejected through the photoelectric effect. Above this

energy, Compton scattering is the dominant mechanism used for electron emission. As an example,

Uehara and Nikjoo (1996) studied the energy spectrum of ejected electrons in the process of photon

interaction with water vapor. In this case, the kinetic energy of the ejected electron is not necessarily

small. But the rst-generation secondary electrons quickly lose their energy through collision with

matter molecules.

3.2.2 colliSion croSS Section and related QuantitieS

All physical phenomena discussed in radiation sciences are analyzed in terms of relevant colli-

sion cross sections. Here, the cross section for an inelastic collision process is dened as follows:

Suppose that I

electrons of energy E

, per unit area per unit time, are incident on a molecular gas

with number density N. The number of electrons scattered per unit time into the solid angular element