Drake G.W.F. (editor) Handbook of Atomic, Molecular, and Optical Physics

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920 Part E Scattering Experiment

n⬘ l⬘ j⬘

nlj

n⬙ l ⬙ j ⬙

∞

Fig. 62.3 Energy levels involved in the direct (D) and ex-

change (E) Auger processes, and notation for the principal,

orbital angular momentum, and total angular momentum

quantum numbers that characterize the pertinent electron

states

state of the continuum (Auger) electron is labeled

by ∞

. In the physically indistinguishable exchange

process, described by a matrix element E, the roles of

electrons n j and n



are interchanged (Fig. 62.3).

The radiationless transition probability per unit time is

2π



D − E







(62.14)

where ρ(E

) is the density of ﬁnal states for the energy

that satisﬁes energy conservation. With the con-

tinuum wave function normalized to one electron ejected

per unit time, we have ρ(E

) = (2π )

−1

([62.22, 52],

Appendix E).

The matrix elements D and E in (62.14) can be sep-

arated into radial and angular factors. Evaluation of the

angular factors depends upon the choice of an appropri-

ate angular momentum coupling scheme [62.1, 51, 53],

ranging from the (LSJM) representation of Russell-

Saunders coupling for the lightest atoms in which the

spin-orbit interaction can be neglected, through inter-

mediate coupling, to j– j coupling in the high-Z limit.

The coupling scheme particularly affects intensity ratios

among multiplet components of Auger spectra, which

can vary by more than an order of magnitude depend-

ing upon its choice. Furthermore, realistic calculations

of Auger energies and rates call for the use of rela-

tivistic wave functions and inclusion of correlation and

relaxation effects [62.1,54]. It is this extreme sensitivity

of Auger transitions to the details of the atomic model

that makes them an exceedingly useful probe of atomic

structure (see also Chapt. 23 and Chapt. 61).

Classiﬁcation of Auger transitions in the central

ﬁeld model is conventionally based on the nomenclature

summarized in Table 62.1.

The spectroscopic notation s, p, d, f,... is em-

ployed for orbital angular momentum quantum numbers

Table 62.1 Nomenclature for vacancy states. The sub-

scripts in the column headings are the values of j = l ± s,

and n is the principal quantum number

n s

1/2

3/2

5/2

7/2

1 K

2 L

3 M

4 N

 = 0, 1, 2, 3,..., and shells with principal quantum

numbers n = 1, 2, 3,... are denoted by K, L, M,....

Let an inner shell vacancy be created initially in a sub-

shell X

and consider a radiationless transition in which

an electron from subshell Y

ﬁlls that vacancy and a

-electron is ejected, in the direct process. This transi-

tion is denoted by X

-Y

, which stands for (n







)

-(n j)(n



) in terms of the vacancies indicated in

Fig. 62.3

Coster–Kronig transitions are a subclass of Auger

transitions in which a vacancy “bubbles up” among

subshells of the same shell, i. e., X

-X

.Theseare

exceptionally fast because the low energy of the ejected

electron tends to prevent cancellations of its wave func-

tion overlap with the other factors in the matrix element

(62.13) and the overlap of the bound state wave functions

can be large owing to their similarity. Coster–Kronig

transitions can therefore lead to hole-state widths in

excess of 10 eV (lifetimes < 10

−16

s) for the L

1,2

sub-

shells of the heaviest elements, for example. McGuire

has coined the name super-Coster–Kronig transitions for

the (even faster) type X

-X

[62.50]. Here the ini-

tial state can no longer be considered quasi-stationary,

the width becomes energy-dependent and the two-step

model breaks down.

The Auger transition energy or kinetic energy of the

ejected electron is, within the central ﬁeld model,

= E







− E

n j,n



, (62.15)

where, in the notation of Fig. 62.3, E







is the ab-

solute value of the energy of the atom with an n







vacancy, with reference to the neutral atom energy, and

n j,n



is the energy of the atom with two vacancies in

the states indicated by the subscripts. This latter energy

can be approximated by a mean of measured single-

ionization energies of the atom under consideration and

that with the next higher atomic number (the “Z + 1

rule” [62.49]); with present-day computers it is readily

calculated through one of the nonrelativistic [62.56, 57]

or relativistic [62.58] self-consistent-ﬁeld codes.

Part E 62.4

Photon–Atom Interactions: Intermediate Energies 62.4 Atomic Response to Inelastic Photon-Atom Interactions 921

Photoionization and, even more so, ionization by

charged particle impact, often produces more than

one vacancy in the target atom (see Sect. 61.1.2 and

Sect. 62.4.4). The ensuing Auger spectrum can then ex-

hibit satellite lines shifted in energy, due to the presence

of spectator vacancies and electrons, with respect to

the diagram lines that arise from the decay of a singly

ionized atom [62.1, 50, 53].

62.4.2 X-Ray Emission

The emission of X-rays by atoms ionized in inner shells

was studied long before the discovery of the much more

probable radiationless transitions, and has played a cru-

cial role in the investigation of atomic structure and

interactions with the environment [62.59]. At present,

X-ray spectrometry is providing important insights into

the structure of highly ionized species produced, e.g.,

in electron beam ion traps [62.60] or plasmas [62.61],

and for the very precise experimental evaluation of

inner-vacancy level energies [62.1, 62].

A classical treatment of multipole radiation by

atomic and nuclear systems is given by Jackson [62.44],

who shows by a simple argument that for atoms the

electric dipole transition rate is ≈ (137/Z

eff

)

times

more intense than electric quadrupole or magnetic

dipole emission, where Z

eff

is the effective (screened)

nuclear charge. The quantum theory of atomic radia-

tion is presented in the treatises by Sakurai [62.63],

Mizushima [62.64], Berestetskii et al. [62.17], and

Sobel’man [62.65], for example. X-ray emission has

been reviewed by Scoﬁeld [62.50, 66] and, with em-

phasis on relativistic effects, by Chen [62.1, 54, 60,

67]. In the present volume, radiative transitions are

treated in Chapt. 33 to which the reader is referred for

details.

62.4.3 Widths and Fluorescence Yields

The energy proﬁle of an atomic hole state that decays

exponentially with time is found to be the same from

quantum as from classical theory [62.68]; it has the

resonance or Lorentz shape

I(ω) dω =

(Γ/2π) d( ω)

( ω − ω

)

. (62.16)

The full width Γ at half maximum of this energy dis-

tribution is proportional to the total decay rate τ

−1

the state, in accordance with Heisenberg’s uncertainty

principle Γτ=

The decay rate τ

−1

= Γ/ of an atomic hole state is

commonly given in units of eV/

or in atomic units (a.u.)

of inverse time, with the corresponding level width Γ

in eV or a.u. Thus, for the decay rate,

= 1a.u. = 4.134 14 × 10

−1

= 27.2116

(62.17)

K-level (1s hole-state) widths increase monotonically

with atomic number, from 0.24 eV for Ne to 96 eV for U,

closely following the approximate relation [62.49]

Γ(1s) = 1.73 Z

3.93

×10

−6

eV . (62.18)

L-subshell widths, as functions of atomic number, ex-

hibit sharp discontinuities that correspond to energetic

cutoffs and onsets of intense Coster–Kronig chan-

nels (Sect. 62.4.1) [62.69].

If there are several decay channels, their partial

widths Γ

add:

Γ =



. (62.19)

The main decay channels for inner shell hole states are

radiative, with a partial width Γ

, and radiationless or

Auger, with a partial width Γ

The ﬂuorescence yield ω

of a hole state i is de-

ﬁned as the relative probability that the state decays

radiatively:

≡ Γ

(i)/Γ (i). (62.20)

Macroscopically, for example, the K-shell ﬂuores-

cence yield ω

is the number of characteristic K

X-ray photons emitted from a sample divided by the

number of primary K-shell vacancies created in the

sample. This ratio rises from 0.04 for Al to 0.97

for U [62.49]. The deﬁnition of ﬂuorescence yields

of shells above the K-shell is more complicated be-

cause the higher shells consist of several subshells and

Coster–Kronig transitions (Sect. 62.4.1) can shift pri-

mary vacancies to higher subshells before they are ﬁlled

radiatively.

The concept of ﬂuorescence yields is useful in many

applications, particularly where the transport of radiant

energy through matter is an issue, as in space sciences,

medical radiology, and some ﬁelds of engineering as

well as in physics. Tables of ﬂuorescence yields can

be found in the review by Bambynek et al. [62.49]

and in the compilations by Krause [62.70]andHubbell

et al. [62.71]. Considerable uncertainty persists in the

ﬂuorescence yields of higher shells.

Part E 62.4

922 Part E Scattering Experiment

62.4.4 Multi-Electron Excitations

In atomic inner-shell photoionization, more than one

electron can be excited with signiﬁcant probability.

Final states are thus produced that can be described

approximately by removal of a core electron and ex-

citation of additional electrons to higher bound states

(shakeup) or to the continuum (shakeoff). These mul-

tiple excitation processes exhibit themselves through

satellites in photoelectron spectra (Sect. 61.1.2)andin

the Auger and X-ray spectra emitted when the ex-

cited states decay, as well as in some cases by features

in absorption spectra [62.72]. As the photon-electron

interaction is described by a one-electron operator,

the frozen-core, central ﬁeld model does not predict

changes of state under photon impact by more than

one electron. Direct multiple excitation processes are

thus a result of electron-electron correlation (Chapt. 23,

Sect. 61.1.2).

Cross sections for photoexcitation and ionization of

two inner shell electrons have been evaluated [62.72]

by the multichannel multiconﬁguration Dirac–Fock

(MMCDF) method [62.73]. Within this model, the corre-

lation effects that cause direct two-electron processes are

(i) relaxation or core rearrangement, (ii) initial state con-

ﬁguration interaction, (iii) ﬁnal ionic state conﬁguration

interaction, and (iv) ﬁnal continuum state conﬁguration,

or ﬁnal state channel interaction.

Mechanisms that contribute to two-electron pho-

toionization of the outermost shells of noble gas

atoms have been separated within many-body per-

turbation theory [62.74]. In ﬁrst order of the

combined perturbations by the photon ﬁeld and

electron correlations, the important contributions are

core rearrangement, initial state correlations, vir-

tual Auger transitions, and “direct collisions” by

the photoelectron with another orbital electron. If

treated nonperturbatively, these mechanisms belong

within the MMCDF scheme to categories (i)–(iv) de-

scribed above. The different mechanisms have been

found to be of varying importance, depending on

the photon energy relative to the double ionization

threshold energy, the orbitals which are ionized, and

the relative ﬁnal state energies of the active elec-

trons. Interest in the theory [62.75, 76] has been

enhanced by experiments with synchrotron radiation

on the double ionization of He [62.77], a process

that epitomizes the problem. Above ≈ 5 keV pho-

ton energy, the double ionization of He has been

shown to be dominated by Compton scattering, not

photoeffect [62.78].

62.4.5 Momentum Spectroscopy

We close with a few examples of fruitful recent advances

in approaches to the study of electron-atom interactions.

A step-function advance in viewing atomic collision

dynamics, including photon-electron interactions, arose

from the development (ﬁrst in the University of Frank-

furt by Schmidt-Böcking and his group) of Cold-Target

Recoil-Ion Momentum Spectroscopy (COLTRIMS), a

“momentum microscope” to view the dynamics of

photon-atom collisions [62.79–81]. This novel momen-

tum space imaging technique allows the investigation

of the dynamics of ion, electron, or photon impact re-

actions with atoms or molecules. Studies performed

with this technique yield kinematically complete pic-

tures of the fragments of atomic and molecular breakup

processes, unprecedented in resolution, detail and com-

pleteness. The multiple-dimensional momentum-space

images often directly unveil the physical mechanism

underlying the many-particle transitions that are being

investigated [62.82]. Important applications are being

developed [62.83, 84].

62.4.6 Ultrashort Light Pulses

Advances in laser technology have made it pos-

sible to obtain high-intensity (up to 10

W/cm

short (5 fs) pulses, making laser-atom [62.85]and

laser-molecule interactions [62.86–89] amenable to

experimental study. In the latter category, nonlinear

phenomena such as above-threshold ionization and

laser-induced molecular potentials have already been

explained theoretically [62.90–92].

Ultrashort light pulses make it possible to follow

ultrafast relaxation processes on never-before-accessed

time scales and to study light-matter interactions at

unprecedented intensity levels [62.85,93].

Ultrafast optics has permitted the generation of light

wave packets comprising only a few oscillation cycles

of the electric and magnetic ﬁelds. The spatial exten-

sion of these wave packets along the direction of their

propagation is limited to a few times the wavelength of

the radiation. The pulses can be focused to a spot size

comparable to the wavelength. Radiation can thus be

temporarily conﬁned to a few cubic micrometers, form-

ing a “light bullet”. The extreme temporal and spatial

conﬁnement allows moderate pulse energies of the or-

der of one microjoule to result in peak intensities higher

than 10

W/cm

. These ﬁeld strengths exceed those of

the static ﬁeld seen by outer-shell electrons in atoms. The

laser ﬁeld consequently is strong enough to suppress the

Part E 62.4

Photon–Atom Interactions: Intermediate Energies 62.5 Threshold Phenomena 923

binding Coulomb potential in atoms and triggers optical

ﬁeld ionization [62.94, 95].

Attosecond



−18



trains from high-harmonic

generation have been discovered [62.90–92]. High har-

monics, generated in a gas jet by a femtosecond laser

pulse, have a well-deﬁned phase relation with respect to

each other. The relative phases result in strong amplitude

beating between the various harmonics. The emerging

radiation thus consists of attosecond pulses.

The process of harmonic generation can be thought

of as consisting of three steps [62.92]: a (rate-limiting)

ﬁeld ionization of the atom at times near the electric

ﬁeld maxima, followed by acceleration of the free elec-

tron which, due to the ac character of the driving light,

eventually makes the electron recollide at high energy

with its parent ion. Radiative recapture of this fast elec-

tron into the ground state, strongly favored due to the

remaining coherence between the two parts of what was

initially the same wave function, completes the harmonic

generation process without any change to the atom.

In summary, intense few-cycle light pulses open

up never yet accessed parameters in high-ﬁeld

physics [62.85]. Strong-ﬁeld processes induced by few-

cycle laser ﬁelds may permit access to the phase of the

carrier wave and hence to the light ﬁelds for the ﬁrst

time. Phase-controlled light pulses may allow control

of high-intensity light-matter interaction on a subcycle

time scale. The search for laser-driven ultrafast X-ray

sources is also drawing beneﬁts from this research area.

Substantial major progress can be anticipated in this new

ﬁeld.

62.4.7 Nondipolar Interactions

A powerful tool for exploring photon-atom in-

teractions has been photoionization of atoms and

molecules [62.96]. Analysis of photoelectron angu-

lar distribution measurements was routinely performed

in the electric-dipole approximation, in which all

higher-order multipoles are neglected [62.97]. While

breakdown of the dipole approximation at higher photon

energies (above 5 keV) was known, so that a proper de-

scription requires inclusion of many multipoles [62.98],

experimental limitations appeared to make such exten-

sion unnecessary. A notable exception was a hint found

by Krause, who noticed deviations from the dipole

approximation in measurements on rare gases using

unpolarized X-rays [62.99].

Only when more sophisticated radiation sources

became available, notably synchrotron radiation, and

advances in detector technology took place, did it

become possible to gain data on nondipolar photoioniza-

tion [62.98]. Intense experimental and theoretical work

ensued.

Photoelectron angular distributions depend upon dy-

namical parameters of the target atoms and upon the

polarization of the photon beam. Peshkin developed a

systematic analysis of the restrictions imposed by sym-

metry, through a geometric description of polarization

that is easily visualized and has been found useful in

planning experiments [62.100].

Earlier theories predicted nondipolar asymmetries

of 1s photoelectron distributions in the point-Coulomb

potential. More recently, photoionization amplitudes

are calculated in screened potentials, predicting richer

Z-dependent and subshell-dependent energy variations

of nondipole asymmetries [62.97]. A full relativis-

tic multipole expansion, incuding screening effects,

in the independent-particle approximation was dis-

cussed by Tseng et al. [62.97]. In addition, leading

correction terms to the dipole approximation can

be included by adopting the “retardation expansion”

of the exponential factor exp(ik· r) [62.101, 102]

which, unlike the multipole expansion, includes a ﬁ-

nite number of multipoles within the long-wavelength

limit [62.103]. A lucid summary of the develop-

ment of the subject can be found in the paper by

Krässig et al.on nondipole asymmetries of Kr 1s photo-

electrons [62.104]. Extending the subject, experiments

and theory on electric-octupole and pure-electric-

quadruple effects on soft-X-ray photoemission have

been described by Derevianko et al. [62.105].

62.5 Threshold Phenomena

During the creation of a core vacancy by photoexci-

tation or ionization, the escape of the photoelectron

from an inner shell involves complex dynamics of

electron excitations with multiple correlational aspects.

The entire process of inner shell photoionization and

subsequent de-excitation has drastically different char-

acteristics near threshold from that in the high energy

limit. In the latter case, discussed in the preceding sec-

tions, if an X-ray photon promotes an inner shell electron

to an energetic continuum state, the atom ﬁrst relaxes in

Part E 62.5

924 Part E Scattering Experiment

its excited (hole) state. In a practically distinct second

step, the hole is then ﬁlled—most often by a radia-

tionless transition, under emission of an Auger electron

with diagram energy that can readily be calculated from

the wave function of the stationary, real intermediate

state [62.1, 53].

On the other hand, in the vicinity of core-level

energy thresholds, atomic photoexcitation and the en-

suing X-ray or Auger electron emission occur in a

single second-order quantum process, the resonant Ra-

man effect. Here, the intermediate states are virtual

and there is no relaxation phase. The resonant Raman

regime, comprising the energy region just below thresh-

old, is linked by the post-collision interaction regime

(Sect. 62.5.2) above threshold to the (asymptotically)

two-step regime.

The primary process of photoionization and Auger

electron emission can be viewed as resonant double pho-

toionization mediated by a complete set of intermediate

states; these correspond to an intermediate virtual inner

shell hole and an electron in excited bound or con-

tinuum states. A uniﬁed treatment of the process, as

well as of resonant X-ray Raman scattering, has been

developed within the framework of relativistic time in-

dependent resonant scattering theory [62.48, 106–108].

As the energy of the incoming photons is increased,

3385

3380

3375

3370

3365

0 10203040

4780 4790 4800 4810 4820 4830

exc

(eV)

Energy

shift ∆

(eV)

X-ray energy ω (eV)

Electron energy (eV)

Theory

Experiment

Diagram line

6d spectator

5d spectator

)

Fig. 62.4 Energy of the Xe L

–M

(

) Auger electron peak, as

a function of exciting photon energy. Near threshold Auger satellites,

caused by the spectator photoelectron in bound orbits, exhibit linear

Raman dispersion. The post-collision interaction shift (right-hand

scale) vanishes only in the asymptotic limit (After [62.83])

sweeping through an inner shell threshold, continuous

asymmetric electron distributions associated with differ-

ent two-hole multiplets evolve into Auger-electron lines

with characteristic energies. The shapes and energies

of the characteristic lines continue to change until the

energy of the photoelectron exceeds that of the Auger

electron. The nonresonant two-electron emission ampli-

tude is usually negligible in this region, compared with

the resonant amplitude.

62.5.1 Raman Processes

Resonant Raman transitions to bound ﬁnal states are

the inelastic analog of resonance ﬂuorescence [62.68],

with which they share two characteristic features:

(1) the emitted radiation can have a narrower bandwidth

than the natural lifetime width of the correspond-

ing diagram line, and (2) the energy of the emitted

radiation exhibits linear dispersion with excitation en-

ergy. Radiative resonant Raman scattering was ﬁrst

observed by Sparks in 1974 [62.109] and subsequently

explored with synchrotron radiation by Eisenberger

et al.(see [62.48, 48, 108, 110]). Radiationless resonant

Raman scattering was identiﬁed by Brown et al. [62.111]

and in subsequent studies [62.112] of the deformation

of Auger-electron lines near threshold (Fig. 62.4). The

connection between resonant Raman and Compton scat-

tering has been pointed out by Bergstrom et al. [62.47].

According to a generalization of time independent

resonant scattering theory [62.106, 107], a transition

matrix element can be constructed that accounts for

photoexcitation and either radiative or radiationless de-

excitation, including resonance structure [62.48, 108].

The wave functions represent both the atomic and photon

ﬁelds and include all electrons throughout the process.

The conventional two-step model of X-ray ﬂuorescence

and Auger electron emission is but a special case of the

transition amplitude

βα



−

βεε









dτ

(H − E)|ψ

τν

ψ

τν

E − E

τν

(E)





(62.21)

where H is the total Hamiltonian, V

the photon-electron

interaction operator, and E =

+ E

is the total en-

ergy. The ﬁrst term in T

βα

represents direct nonresonant

Raman scattering; the resonance behavior is embedded

in the second amplitude. The complex eigenenergies

τν

(E) satisfy a complicated secular equation that in-

volves diagonal and nondiagonal matrix elements of the

level shifts and widths [62.1,3, 48, 108]. The initial state

Part E 62.5

Photon–Atom Interactions: Intermediate Energies References 925

wave function ψ

is a direct product of the initial atomic

state wave function and a one-photon state |k

,where

is the wave vector and e

, the polarization vector. The

ﬁnal state scattering wave function ψ

−

βεε



corresponds,

in the radiative case, to a scattered photon in a deﬁnite

state |k

 and an electron plus ion in a given quantum

state, which may involve the linear momentum

the electron if the latter is in the continuum. In the radi-

ationless case, there are an ion and two electrons, both

of which may be in a continuum state |k

, k



.Thewave

function ψ

−

βεε



fulﬁlls the ingoing-wave boundary con-

dition with respect to the electron(s) and accounts for

ﬁnal state channel interaction effects.

Work on inner shell Raman processes is as yet in

its infancy. Synchrotron radiation experiments, inter-

preted in light of the theory outlined above, promise

to become a useful tool in atomic physics and materials

science [62.113, 114].

62.5.2 Post-Collision Interaction

In the radiationless decay of an atom that has been pho-

toionized near an inner shell threshold, the Coulomb

ﬁeld of the receding photoelectron perturbs the Auger

electron energy and line shape. This post-collision in-

teraction provides continuity in the energy evolution of

inner shell dynamics between the Raman and asymptotic

two-step regimes. In Auger decay, following photoion-

ization, the Auger electron initially screens the ionic

Coulomb ﬁeld seen by the receding photoelectron. This

screening subsides when the (usually fast) Auger elec-

tron passes the slow photoelectron. Distortion of the

Auger line shape results, and the Auger energy is raised

at the expense of the photoelectron energy (Fig. 62.4).

A semiclassical potential curve model of post-

collision interaction leads to intuitive insight and

surprisingly accurate predictions [62.115, 116]. In sim-

ple terms, the attractive potential well in which the slow

photoelectron moves is deepened suddenly when the

residual singly ionized atom undergoes Auger decay

and its net charge changes from +e to +2e. The pho-

toelectron sinks down into this deeper well, there being

no time for it to speed up, and the energy lost by the

photoelectron is transferred to the Auger electron. The

photoelectron slows down and may even be recaptured

by the atom from which it was emitted [62.117].

Quantum theoretically, post-collision interaction can

be treated from the point of view of resonant scattering

theory (Sect. 62.5.1). A lowest-order line shape for-

mula, corresponding to a shakedown mechanism, can

be shown to emerge from approximations of the gen-

eral multichannel transition matrix element [62.118];

the phenomenon thus arises as a consequence of a reso-

nant rearrangement collision in which a photon and an

atom in the initial channel turn into an ion and two elec-

trons (one of which has nearly characteristic energy) in

the ﬁnal channel. In this lowest order, the results can be

interpreted in terms of an analytic line shape formula

based on asymptotic Coulomb wave functions [62.118].

The line shape depends only on the excess photon en-

ergy, the lifetime of the initial state of the Auger process,

and the change of the ionic charge during Auger electron

emission.

The interaction between the photoelectron and the

Auger electron in the ﬁnal state can be included by rein-

terpreting the ionic charge seen by the photoelectron

on the basis of asymptotic properties of the continuum

wave function pertaining to the two outgoing elec-

trons [62.119, 120]. This results in a procedure which

is consistent with semiclassical models that account for

the time required for the Auger electron to overtake

the photoelectron. Calculations based on this approach

agree very well with measurements performed with

synchrotron radiation [62.120].

References

62.1 L. Kissel, R. H. Pratt: In: Atomic Inner-Shell Physics,

ed. by B. Crasemann (Plenum, New York 1985)

Chap. 11

62.2 L. Kissel, R. H. Pratt, S. C. Roy: Phys. Rev. A 22,1970

(1980)

62.3 J. Tulkki, T. Åberg: [62.1, Chap. 10]

62.4 V. A. Bushuev, R. N. Kuz’min: Sov. Phys. Usp. 20,

406 (1977)

62.5 K.-I. Hino, P. M. Bergstrom Jr., J. H. Macek: Phys.

Rev. Lett. 72, 1620 (1994)

62.6 For up-to-date atomic data see Photon Inter-

action Data (EPDL97); Electron Interaction Data

(EEDL), Atomic Relaxation Data (EADL). Contact

for users within the U.S.A.: National Nuclear

Data Center (NNDC), Brookhaven National Labora-

tory, Vicki McLane, services@bnlnd2.dne.bnl.gov.

Contact for users outside the U.S.A.: Nuclear

Data Section (NDS), International Atomic Energy

Agency (IAEA), Vienna, Austria, Vladimir Pronyaev,

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Part E 62

929

Electron–Atom

63. Electron–Atom and Electron–Molecule Collisions

Electron–atom and electron–molecule collision

processes play a prominent role in a variety

of systems ranging from discharge or electron-

beam lasers and plasma processing devices

to aurorae and solar plasmas. Early studies of

these interactions contributed signiﬁcantly to the

understanding of the quantum nature of matter.

Experimental activities in this ﬁeld, initiated by

Franck and Hertz [63.1], ﬂourished in the 1930s

and, after a dormant period of about a quarter

of a century, have had a renaissance in recent

years.

When electrons collide with atomic or mo-

lecular targets, a large variety of reactions can

takeplace(seeSect.63.1.1). We limit our dis-

cussion to electron collisions with gaseous

targets, where single collision conditions pre-

vail. Furthermore, we discuss only low-energy

(threshold to few hundred eV) impact processes

where the interaction between the valence-shell

electrons of the target and the free electron

dominates.

Comprehensive discussions on electron–atom

(molecule) collision physics can be found in the

books of Massey et al. [63.2], McDaniel [63.3]and

the volumes of Advances in Atomic and Molecular

(since 1990 Atomic, Molecular and Optical) Physics.

The latest developments are usually published in

63.1 Basic Concepts..................................... 929

63.1.1 Electron Impact Processes .......... 929

63.1.2 Deﬁnition of Cross Sections......... 929

63.1.3 Scattering Measurements ........... 930

63.2 Collision Processes ............................... 933

63.2.1 Total Scattering Cross Sections..... 933

63.2.2 Elastic Scattering Cross Sections... 933

63.2.3 Momentum Transfer Cross

Sections ................................... 933

63.2.4 Excitation Cross Sections ............ 933

63.2.5 Dissociation Cross Sections ......... 935

63.2.6 Ionization Cross Sections ............ 935

63.3 Coincidence and Superelastic

Measurements..................................... 936

63.4 Experiments with Polarized Electrons .... 938

63.5 Electron Collisions

with Excited Species ............................ 939

63.6 Electron Collisions in Traps ................... 939

63.7 Future Developments ........................... 940

References .................................................. 940

Physical Review A, Journal of Physics B, Journal

of Chemical Physics and Journal of Physical and

Chemical Reference Data, and are presented at the

biannual International Conference on Photonic,

Electronic and Atomic Collisions (ICPEAC).

63.1 Basic Concepts

63.1.1 Electron Impact Processes

Lox energy electrons can very effectively interact with

the valence-shell electrons of atoms and molecules, in

part because they have similar speeds. In elastic scat-

tering, the continuum electron changes direction and

transfers momentum to the target. Inelastic collisions

include also a transfer of kinetic energy to the target,

such as excitation of valence electrons to discrete en-

ergy levels, to the ionization continuum, and, in the case

of molecules, excitation of nuclear motion (rotational,

vibrational) and excitation to states which dissociate

into neutral or ionic fragments. Various combinations

of these processes are also possible, e.g., dissociative at-

tachment, excitation or ionization. Excitation of more

than one valence electron at the same time, or excitation

of electrons from intermediate and inner shells, may also

occur but these processes are more likely at impact en-

ergies of a few keV. These excitations lie above the ﬁrst

ionization limit and lead, therefore, with high probabil-

ity, to autoionization, except for heavy elements where

X-ray emission is an important competing process.

Part E 63