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

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940 Part E Scattering Experiment

63.7 Future Developments

Electron-driven processes have been identiﬁed as being

of fundamental importance in a wide range of environ-

mentally and technologically signiﬁcant areas [63.77].

Boudaiffa et al. [63.78] have shown that electron at-

tachment is a signiﬁcant process in bond-breaking in

DNA. Electron-initiated dissociation of large molecules

can act as a catalyst for reactive chemistry in envi-

ronmentally sensitive situations. Developments in large

scale computing have opened the door to calculations

involving large molecules which could not even have

been contemplated a few years ago. Electron colli-

sions in intense laser ﬁeld situations is an exciting new

ﬁeld which is rapidly expanding [63.79, 80]. Electron–

cluster interactions allow one to probe how interactions

change as one progresses from the gaseous to the solid

phase.

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Part E 63

943

Ion–Atom Scat

64. Ion–Atom Scattering Experiments: Low Energy

This chapter outlines the physical principles

and experimental methods used to investigate

low energy ion–atom collisions. A low energy

collision is here deﬁned as one in which the

initial ion–atom relative velocity is less than

the mean orbital velocity v

 of the electrons

affected by the collision. For outer or valence

electrons, v

v

,wherev

= 2.1877× 10

cm/s

is the Bohr velocity. In terms of the energy of

a projectile ion, v

corresponds to 24.8keV/N,

where N is the projectile nuclear number (e.g.,

16 for O

The theory and results of ion–atom scatter-

ing studies are further discussed in Chapts. 37,

38,and47 to 51.Thefocushereisontheex-

perimental techniques. Since several of these

depend on the characteristics of a speciﬁc pro-

cess, the following section presents a summary

of the physics of low-energy ion–atom colli-

sions. See Chapts. 50 and 51 for more detailed

information.

64.1 Low Energy Ion–Atom Collision Processes 943

64.2 Experimental Methods

for Total Cross Section Measurements .... 945

64.2.1 Gas Target

Beam Attenuation Method ......... 945

64.2.2 Gas Target

Product Growth Method ............. 945

64.2.3 Crossed Ion

and Thermal Beams Method ....... 945

64.2.4 Fast Merged Beams Method........ 946

64.2.5 Trapped Ion Method .................. 946

64.2.6 Swarm Method ......................... 947

64.3 Methods for State

and Angular Selective Measurements .... 947

64.3.1 Photon Emission Spectroscopy .... 947

64.3.2 Translational Energy Spectroscopy 947

64.3.3 Electron Emission Spectroscopy ... 948

64.3.4 Angular Differential

Measurements .......................... 948

64.3.5 Recoil Ion Momentum

Spectroscopy ............................ 948

References .................................................. 948

64.1 Low Energy Ion–Atom Collision Processes

The most important and widely studied inelastic ion–

atom collision process in the low energy region is

electron capture (also referred to as charge exchange,

charge transfer or electron transfer) represented by

+ B → A

+q−k

+ B

+ Q , (64.1)

where Q is the potential energy difference between the

initial and ﬁnal states. For an exoergic process, Q > 0

and this energy appears as excess kinetic energy of the

products after the collision. For an endoergic process,

Q < 0 and must be provided by the initial kinetic en-

ergy of the reactants, so that the corresponding cross

section is usually small at low collision energies. Cross

sections for electron capture are appreciable even at very

low energies if Q is zero or very small (resonant or near-

resonant process). Electron capture by multiply charged

ions from atoms is predominantly an exoergic process,

for which cross sections may also be large at low ener-

gies. In this case, electrons are preferentially captured

into excited levels of A

+q−k

. The typical cross section

behavior for single electron capture (k = 1) by a multiply

charged ion from atomic hydrogen is shown in Fig. 64.1.

The initial ionic charge is the major determinant of the

cross section at intermediate and high collision ener-

gies, whereas the cross section at low energies depends

strongly on the structure of the transient quasimolecule

formed during the collision.

Multiple electron capture (k > 1) from multielectron

atoms occurs predominantly into multiply excited levels,

which stabilize either radiatively, leading to stabilized or

“true” double capture, or via autoionization. The latter

process is usually referred to as transfer ionization,

+ B → A

+q−k

+ B

+ (m − k)e

−

+ Q .

(64.2)

At low energies, transfer ionization is particularly

important in collisions of highly charged ions with

multi-electron atoms.

Part E 64

944 Part E Scattering Experiment

–13

–14

–15

–16

–17

–18

–19

Cross section (cm

)

Collision energy (eV/u)

q ×10

–15

+ Η A

(q–1)+

+ Η

Fig. 64.1 Typical cross section variation with collision

energy for electron capture by a multiply charged ion

from hydrogen. The low energy behavior depends on

the structure of the quasimolecule formed during the

collision

Adiabatic potential energy curves representing the

collision of a multiply charged ion with a neutral

atom are presented in Fig. 64.2. For such collisions, the

Coulomb repulsion in the ﬁnal state produces avoided

crossings of the initial and ﬁnal state potential curves,

the positions of which are determined by the binding

energy of the atomic electron and electronic energy

level structure of the product ion. Generally, reac-

tion channels that are moderately exoergic produce

curve crossings at internuclear separations where there

is sufﬁcient overlap of the electron clouds for elec-

tron capture to be a likely process. The Landau–Zener

curve-crossing model [64.1](Chapt.49), the classical

over-barrier model for single capture [64.2]andthe

extended classical over-barrier model for multiple cap-

ture [64.3], are useful in predicting the important ﬁnal

product states, and in providing a semiquantitative inter-

pretation. In the case of single electron capture by a bare

multiply charged ion (of charge q = Z) from a hydro-

gen atom, the principal quantum number n

of the most

probable ﬁnal ionic state is given in this model [64.2]



1/2

+ 1

Z + 2Z

1/2

. (64.3)

–1

–2

Internuclear separation (a.u.)

12 4 102040

Potential energy (a.u.)

+q–1

+ B

+q–1

+ B

+q–2

+ B

+q–1

+ B

+q–2

+ B

Fig. 64.2 Schematic representation of potential energy

curves for the collision of a multiply charged ion A

with

a multielectron atom B

The internuclear separation R

at which the potential

curves cross in this case is given by

2(Z − 1)

− 1

(64.4)

There has been much discussion of the role of elec-

tron correlation in the multiple electron capture process.

At issue is the relative importance of the mechanism

whereby several electrons are transferred (in a cor-

related manner) at a single curve crossing compared

with that whereby single electrons are transferred suc-

cessively at different curve crossings. Experimental

evidence exists for both mechanisms, with the rela-

tive importance depending on the electronic structure

of the transient quasimolecule that is formed during the

collision. Measurements of the distribution of ﬁnal ion

product electronic states provides the major insight into

such collision mechanisms [64.4].

Other inelastic ion–atom collision processes, such

as direct electronic excitation and ionization, are endo-

thermic, with relatively small cross sections that fall

off with decreasing energy below a few tens of keV/N.

Exceptions are collisions involving Rydberg atoms and

collisional excitation of ﬁne structure transitions, for

which the required energy transfer is relatively small.

Relatively little experimental data are available for di-

rect excitation and ionization processes at low collision

energies.

Part E 64.1

Ion–Atom Scattering Experiments: Low Energy 64.2 Experimental Methods for Total Cross Section Measurements 945

64.2 Experimental Methods for Total Cross Section Measurements

In the present context, a total cross section measurement

refers to an integration or summation over scattering

angles, product kinetic energies and (frequently) elec-

tronic states. The total cross section is usually measured

as a function of relative collision energy or velocity.

64.2.1 Gas Target

Beam Attenuation Method

The attenuation of a collimated ion beam of incident

intensity I

in a differentially pumped gas target cell or

gas jet is related to the collision cross section σ by

I = I

−σNL

, (64.5)

where I is the intensity after traversing an effective

length L of the target gas, and N is the number density of

target atoms. For a gas target cell with entrance and exit

apertures of diameter d

and d

which are much less than

the physical length z of the gas cell, L is given to a good

approximation by z + (d

+ d

)/2. This is valid under

molecular ﬂow conditions, for which the mean free path

between collisions of target atoms is much larger than

the dimensions of the gas cell.

In designing the gas cell for measurements of to-

tal cross sections, d

and the beam detector must be

large enough that elastic scattering may be eliminated

as a contributor to the measured attenuation. Usually

is made larger than d

. Measurement of the gas pres-

sure in a target cell is usually made using a capacitance

manometer connected to the cell via a tube whose con-

ductance is much larger than that of the gas cell apertures

so that, to a good approximation, the pressure will be the

same in both the manometer and the gas cell. For gas jet

targets, the effective target thickness NL is usually de-

termined by in situ normalization to some well-known

cross section.

The quantity σ in (64.5) refers to an effective cross

section for removing projectile ions from the incident

beam, which is the sum of cross sections for all such

processes. In many cases, a single process (e.g., electron

capture) is dominant, and σ primarily describes that pro-

cess. Whether a collision process removes a projectile

ion from the reactant beam or not depends on the con-

ﬁguration of the experiment. For example, the projectile

particle may remain physically in the beam after pass-

ing through the target, but with a changed charge due to

a collision. This would be registered as an attenuation

of the primary ion beam if the beam is charge analyzed

after the reaction.

64.2.2 Gas Target Product Growth Method

The product growth method is similar to the beam at-

tenuation method; the major difference that the growth

of reaction products is measured rather than the loss of

reactant projectiles. The products may be derived from

either the projectile beam or the gas target, or both. The

main advantage of this method is its higher degree of se-

lectivity of a speciﬁc collision process. In addition, the

reactants and products can usually be registered simul-

taneously, or in some cases in coincidence, eliminating

the sensitivity of the measurement to temporal variation

of ion beam intensity.

An important criterion is that the target gas density

be low enough that single collision conditions prevail

(i. e. that the likelihood of an ion passing through the

gas target and interacting with more than one target

atom is negligibly small). This must in general be satis-

ﬁed in order for (64.5) to relate correctly the measured

attenuation to the collision cross section of interest, and

is critical to the product growth method [64.5]. In this

case, under single collision conditions, one may set the

number of products I

= I

− I,and(64.5) then may be

written as

= 1 − e

−σNL

≈ σNL . (64.6)

The approximate expression is useful for σNL  1,

which is a requirement for single collision conditions. It

is also important that the products not be lost in a sub-

sequent collision in the gas cell, so the magnitudes of

cross sections for loss of products in the target gas must

also be considered. The products in such an experiment

may be derived from either the projectile beam or the

target gas (e.g., collection of slow product ions in a gas

cell), or from both in coincidence to enhance the speci-

ﬁcity of the method. The method may in principle be

used to determine either total or differential cross sec-

tions, depending on the degree of selectivity of collision

products.

64.2.3 Crossed Ion

and Thermal Beams Method

Replacement of the gas target cell by an effusive ther-

mal beam is advantageous for studying collisions of ions

with reactive species such as atomic hydrogen, as well as

for collecting slow ion products. The use of accelerating

electrodes or grids for slow charged products allows co-

incident detection of fast and slow products, permitting

Part E 64.2

946 Part E Scattering Experiment

measurement of ionization as well as electron-capture

cross sections. Use of an effusive source or gas jet

precludes accurate measurement of the effective target

thickness, and in situ normalization to the cross sec-

tion for some well known process is usually employed.

A comprehensive discussion of such methods as ap-

plied to collisions of multiply charged ions with atomic

hydrogen is given by Gilbody [64.6].

64.2.4 Fast Merged Beams Method

Cross sections for ion–atom collision processes at very

low energies have been measured by merging fast beams

of ions and neutral atoms [64.7], as in Fig. 64.3.Inthis

case, σ is determined from experimental parameters by

σ =



− v

F ,

(64.7)

where R is the number of products detected per second,

 is the product detection efﬁciency, e is the electronic

charge, I

is the ion current, I

is the ﬂux of atoms,

and v

are the laboratory velocities of the ion and

atom beams, v

rel

is their relative velocity, and F is the

form factor that describes the spatial overlap of the two

beams. If the z-axis is chosen to be the direction of

propagation of the beams, the form factor has units of

length and is given by

F =



(x, y, z) dx dy



(x, y, z) dx dy



(x, y, z)I

(x, y, z) dx dydz

(64.8)

The two-dimensional integrals in the numerator repre-

sent the total intensities of the two beams, which are

independent of z,sothatF is also independent of z.

Collision region

(50 cm)

Neutral

beam detector

Faraday cup

Channel electron

multiplier

(q–1)+

Fig. 64.3 Schematic of the merged beams arrangement

used by Havener et al. [64.7] to study low energy electron

capture collisions of multicharged ions with H atoms

The relative collision energy E

rel

in eV/uisgiven

rel

− 2



cos θ, (64.9)

where E

, m

and E

, m

are the energies and masses

of the ion and atom, respectively, and µ is their reduced

mass. For collinear merged beams, θ = 0, and E

rel

can

be reduced to zero by making the two beam veloci-

ties the same. In practice, the ﬁnite divergences of the

beams place a lower limit on the energy and the energy

resolution. The fast neutral atom beam is created by

neutralizing an accelerated ion beam by electron capture

by a positive ion beam in a gas, by electron detachment of

a negative ion beam either in a gas, or using a laser beam.

In gas collisions, a small fraction of the neutral beam is

produced in excited n-levels (with an n

−3

distribution),

which may inﬂuence the measurements.

With fast colliding beams, the maximum effective

beam densities are invariably much smaller than the

background gas density, even under ultrahigh vacuum

conditions. For example, a typical 10 keV proton beam

with a circular cross section of diameter 3 mm and

a current I = 10 µA has an average effective density

n = I/(eAv) = 1.6×10

−3

(A is the beam cross sec-

tional area and v is its velocity). It is therefore necessary

either to modulate the beams or to use coincidence

techniques to separate signal events due to beam–beam

collisions from background events produced by colli-

sions of either beam with background gas. A typical

two-beam modulation scheme is shown in Fig. 64.4.To

eliminate the production of spurious signals, the detec-

tor gates are delayed for a short time after the beams are

switched, and the beam modulation period is made much

shorter than the pressure time constant of the vacuum

system.

Absolute electron-capture cross sections have been

measured for O

+ H collisions to energies below

1eV/N, where the attractive ion-induced-dipole (polar-

ization) interaction is expected to play a role [64.7]. The

inverse velocity dependence of the cross section in this

region is suggestive of the classical Langevin orbiting

model for ion–neutral collisions [64.8].

64.2.5 Trapped Ion Method

The trapped ion method is used to determine rate co-

efﬁcients and effective cross sections for ion–atom

collisions at near thermal energies. The technique in-

volves storing ions in an electrostatic or electromagnetic

Part E 64.2

Ion–Atom Scattering Experiments: Low Energy 64.3 Methods for State and Angular Selective Measurements 947

Atom

beam

Ion

beam

Scaler

No. 1

Scaler

No. 2

Off

22 µ s

Fig. 64.4 Fast two-beam modulation scheme to separate

the signal due to beam–beam collisions from events due to

beam collisions with residual gas or surfaces [64.7]

trap, and measuring the rate of loss of ions from the trap

after a small quantity of neutral gas is admitted [64.9].

Like the beam attenuation method, the trap technique

cannot distinguish different processes that cause ions

to be lost from the trap. The mean collision energy is

estimated from an analysis of the ion dynamics in the

trap.

64.2.6 Swarm Method

The swarm method, using the ﬂowing afterglow, drift

tube or selected-ion ﬂow tube, has been used suc-

cessfully to study ion–atom collisions at very low

energies [64.10]. Ions are injected into a homogeneous

electric ﬁeld and drift through a suitable low-density

buffer gas such as helium. The ions move as a swarm

whose mean energy depends on the applied electric ﬁeld

and on collisions with the buffer gas, and can be varied

from the near-thermal region to tens of eV. The method

involves measuring the additional attenuation of the di-

rected ion swarm by a known quantity of added reactant

gas, and is the major technique that has been used for

the study of ion–atom collisions at near-thermal ener-

gies [64.11]. As with ion beam attenuation and ion trap

methods, the drift tube is not selective of the process that

leads to attenuation of the ion swarm.

64.3 Methods for State and Angular Selective Measurements

Three principal methods have been developed and ap-

plied to the measurement of partial cross sections

for population of speciﬁc product electronic states in

ion–atom collisions involving electron capture [64.12].

These are based on spectroscopic measurements of

photon emission, translational energy spectroscopy and

electron emission in collisions of ion beams with gas

targets.

64.3.1 Photon Emission Spectroscopy

Since electron capture from atoms by multiply charged

ions populates excited levels, photon emission spec-

troscopy may be employed to determine state-selective

partial cross sections [64.13]. An ion beam is directed

through a gas cell or jet, and a photomultiplier or suit-

able detector registers photons analyzed by an optical

ﬁlter, a grating or a crystal spectrometer. The measured

photon signal at a given angle depends on the detection

solid angle, the polarization of the emitted radiation, the

absolute efﬁciencies of the dispersive device and de-

tector, and (for emission by fast ions) the lifetime of

the radiating state. Depending on the spectral region,

the photon detection system may be absolutely cali-

brated using a standard photon source or detector, or by

using a reference ion or electron beam and well estab-

lished cross section data for photon emission [64.14].

Cascading from higher populated levels must also be

considered whenever measured spectral line emission

intensities are used to infer cross sections for populating

speciﬁc energy levels. Successful state-selective cross

section measurements have been made for transitions in

the visible, VUV and X-ray spectral regions.

64.3.2 Translational Energy Spectroscopy

Translational energy loss or energy gain spectroscopy

provides a convenient method to determine the distri-

bution of ﬁnal states in low energy ion–atom collisions

that are either endoergic or exoergic (Q = 0). For ex-

ample, this method has been used extensively by the

Belfast group [64.15] to study the predominantly exo-

ergic process of electron capture by multiply charged

ions from hydrogen atoms. An ion beam with a well de-

ﬁned energy is directed through a gas target, and the

energy of the product ion beam is energy analyzed after

the collision. Since the energy gain or loss to be meas-

ured is only a very small fraction of the initial kinetic

Part E 64.3

948 Part E Scattering Experiment

energy, it is usually necessary to reduce the initial en-

ergy spread to a few tenths of an eV by decelerating

the reactant ion beam prior to energy selection by an

electrostatic analyzer. If the scattering angle of the ion

is very small, its energy change is approximately equal

to Q. Since the ion beam is attenuated by deceleration

and energy analysis, cross sections for collisionally pop-

ulating speciﬁc states are determined by normalizing the

measured product-state distributions to total cross sec-

tion data. The attainable state resolution is not as good

as for photon emission spectroscopy.

64.3.3 Electron Emission Spectroscopy

As noted in Sect. 64.1, multiple electron capture by mul-

tiply charged ions from atoms at low energies occurs

primarily into multiply excited states, which decay ei-

ther radiatively or via autoionization (with a branching

ratio) [64.4]. The latter decay pathway (transfer ioniza-

tion) provides an experimental method to determine the

product ionic states by ejected-electron spectroscopy.

Analysis of electrons emitted into the forward (ion

beam) direction (zero degree spectroscopy) offers sig-

niﬁcant advantages for analysis of low energy electrons

with high resolution [64.16]. Since a gas jet is often

employed and absolute electron collection and spec-

trometer efﬁciencies are difﬁcult to determine, some

normalization procedure is usually employed to de-

termine state-selective cross sections by this method.

Electrons and product projectile or recoil ions have also

been detected in coincidence to increase the speciﬁcity

of the method.

64.3.4 Angular Differential Measurements

The measurement of angular distributions of scattered

ions in low energy ion–atom collisions has been facil-

itated by the availability of position-sensitive particle

detectors consisting of a microchannel plate and a re-

sistive or segmented anode [64.17]. The method for

processes that have forward-peaked angular distribu-

tions involves directing a highly collimated ion beam

through a gas target cell, and counting the scattered

projectile ions on a position-sensitive particle detector.

Product ions produced by electron capture can be se-

lected by the use of electrostatic retarding grids mounted

immediately in front of the detector, to reject the primary

ion beam.

64.3.5 Recoil Ion Momentum Spectroscopy

Perhaps the most signiﬁcant experimental development

of the last decade, cold target recoil-ion momentum

spectroscopy (COLTRIMS) [64.18] has been made pos-

sible by advances in position-sensitive particle detection.

This technique, based on momentum imaging and also

called a “reaction microscope”, has yielded important

new insights into the dynamics of ion–atom collision

processes [64.19] as well as other types of interactions

involving cold atoms and molecules. The method is

particularly suited to studies of charge-changing and

molecular fragmentation processes.

In this method, an ion beam intersects a cold su-

personic atomic beam in an interaction volume within

which small electric and magnetic ﬁelds are imposed in

order to guide slow ions and ejected electrons to fast

position-sensitive detectors. The charge and the trans-

verse and longitudinal components of the momentum

of the slow (recoil) ion are measured by a combination

of position and time-of-ﬂight measurements, permitting

the Q-value of the collision and the ﬁnal electronic states

of the projectile and recoil ions to be uniquely deter-

mined. The position measurement additionally provides

information about the angular scattering during the colli-

sion. Coincident measurement of the scattered projectile

ion and determination of its charge state by electro-

static deﬂection, and/or time-of-ﬂight measurements of

ejected electrons have provided new insights into com-

plex multielectron processes occurring in low-energy

ion–atom collisions.

References

64.1 F. W. Meyer, A. M. Howald, C. C. Havener, R. A. Pha-

neuf: Phys. Rev. Lett. 54, 2663 (1985)

64.2 H. Ryufuku, K. Sasaki, T. Watanabe: Phys. Rev. A

23,745(1980)

64.3 A. Niehaus: J. Phys. B 19, 2925 (1986)

64.4 M. Barat, P. Roncin: J. Phys. B 25, 2205 (1992)

64.5 H. B. Gilbody: Adv. At. Mol. Phys. 22,143(1986)

64.6 F. W. Meyer, A. M. Howald, C. C. Havener, R. A. Pha-

neuf: Phys. Rev. A 32, 3310 (1985)

64.7 C. C. Havener, M. S. Huq, H. F. Krause, P. A. Schulz,

R. A. Phaneuf: Phys. Rev. A 39, 1725 (1989)

64.8 G. Gioumoussis, D. P. Stevenson: J. Chem. Phys. 29,

294 (1958)

64.9 D. A. Church: Phys. Rep. 228, 254 (1993)

Part E 64

Ion–Atom Scattering Experiments: Low Energy References 949

64.10 Y. Kaneko: Comm. At. Mol. Phys. 10,145(1981)

64.11 W. Lindinger: Phys. Scrip. T 3, 115 (1983)

64.12 R. K. Janev, H. Winter: Phys. Rep. 117, 266–387

(1985)

64.13 D.

Ciri

c, A. Brazuk, D. Dijkkamp, F. J. de Heer,

H. Winter: J. Phys. B 18, 3639 (1985)

64.14 B. Van Zyl, G. H. Dunn, G. Chamberlain,

D. W. O. Heddle: Phys. Rev. A 22, 1916 (1980)

64.15 H. B. Gilbody: Adv. At. Mol. Opt. Phys. 32,149

(1994)

64.16 N. Stolterfoht: Phys. Rep. 146,316(1987)

64.17 L. N. Tunnell, C. L. Cocke, J. P. Giese, E. Y. Kamber,

S. L. Varghese, W. Waggonner: Phys. Rev. A 35,3299

(1987)

64.18 R. Dörner, V. Mergel, O. Jagutzki, L. Spielberger,

J. Ullrich, R. Moshammer, H. Schmidt-Böcking:

Phys. Rep. 330, 95 (2000)

64.19 J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L. Ph.

H. Schmidt, H. Schmidt-Böcking: Rep. Prog. Phys.

66, 1463 (2003)

Part E 64

951

Ion–Atom Coll

65. Ion–Atom Collisions – High Energy

This chapter deals with inelastic processes which

occur in collisions between fast, often highly

charged, ions and atoms. Fast collisions are here

deﬁned to be those for which V/v

≥ 1, where V is

the projectile velocity and v

the orbital velocity

of this electron. For processes involving outer

shell target electrons, this implies V

 1 a.u., or the

projectile energy

 25 keV/a.m.u. For inner shell

electrons, typically, V

 Z

/n a.u., where Z

is the

target nuclear charge and n the principal quantum

number of the active electron. A useful relationship

is V = 6.35

√

E/M,whereV is in a.u., E is in MeV, and

M is in a.m.u. Fast collisions involving outer shell

processes can be studied using relatively small

accelerators, while those involving inner shell

processes require larger van de Graaffs, LINACs, etc.

Because the motion of the inner shell electrons

is dominated by the nuclear Coulomb ﬁeld of

the target, and because transitions involving

these electrons take place rather independently

of what transpires with the outer shell electrons,

it has proven somewhat easier to understand one

electron processes involving inner shell electrons.

Thus, for a long time, a great deal of the work

on fast ion–atom collisions has concentrated

on inner shell processes involving heavy target

atoms. However, more recently, new experimental

techniques have led to a shift of this focus to

65.1 Basic One-Electron Processes ................ 951

65.1.1 Perturbative Processes ............... 951

65.1.2 Nonperturbative Processes ......... 955

65.2 Multi-Electron Processes ...................... 957

65.3 Electron Spectra in Ion–Atom Collisions . 959

65.3.1 General Characteristics............... 959

65.3.2 High Resolution Measurements ... 960

65.4 Quasi-Free Electron Processes

in Ion–Atom Collisions ......................... 961

65.4.1 Radiative Electron Capture ......... 961

65.4.2 Resonant Transfer and Excitation 961

65.4.3 Excitation and Ionization ........... 961

65.5 Some Exotic Processes .......................... 962

65.5.1 Molecular Orbital X-Rays ............ 962

65.5.2 Positron Production

from Atomic Processes ............... 962

References .................................................. 963

inelastic processes involving light target atoms.

Furthermore, present investigations go beyond

the one-electron picture to include the inﬂuence

of the electron–electron interaction. The present

chapter outlines some of the developments in

this area over a very active past few decades. The

literature is vast, and only a small sampling of

references is given. Emphasis is on experimental

results (for the theory see Chapts. 45–57)

65.1 Basic One-Electron Processes

65.1.1 Perturbative Processes

Inner Shell Ionization of Heavy Targets

For ion–atom collisions involving projectile and target

nuclear charges Z

and Z

respectively, the param-

eters η





)



and η







are

useful in characterizing the strength of the interaction

between Z

, Z

, and the target electron. If η

 η

(i. e., Z

 V/v

), the effect of the projectile on the

target wave function can be treated perturbatively. Per-

turbation treatments of inner shell ionization by lighter

projectiles have been extensively studied and reviewed

[65.1–8]. Two well-known formulations have been used:

the plane wave Born approximation (PWBA) [65.1–4],

and the semiclassical approximation (SCA) [65.9, 10].

The former represents the nuclear motion with plane

waves, while the latter is formulated in terms of the

impact parameter b with the nuclear motion treated clas-

sically. For straight line motion of the nuclei, the results

are equivalent [65.11]. The total cross section for ioniz-

ing the K-shell of a target of charge Z

by a projectile

of charge Z

is given within the PWBA by



8πZ



f(θ

,η

) a

, (65.1)

Part E 65