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

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Collisional Broadening of Spectral Lines 59.5 One-Perturber Approximation 887

Adiabatic states of the diatomic molecule formed by the

emitter-perturber system are considered in which the to-

tal spin is assumed to be decoupled from the total orbital

angular momentum of the electrons. The coupling be-

tween rotational and electronic angular momentum can

also be neglected, because typically, contributions to the

lineproﬁlecomefrom0≤l

 400, whereas Λ

 2.

Therefore, transitions take place between channels de-

ﬁned by

= Λ

, j = i, f , (59.118)

where the unperturbed emitter in state j has quan-

tum numbers L

S, the quantum number Λ

represents

the projection of the orbital angular momentum on the

internuclear axis, and (59.100) is replaced by

(

r, R

)

= O



(

r; R

)



, k

; R



(59.119)

where k

= k

and ψ

(

r; R

)

is the wave function for

molecular state Λ

. In (59.119), the only molecular

states retained are those that correlate with emitter states

i and f . The scattering is described by



−





−

2µ

(

)



× F

(

)

= 0 ,

(59.120)

where k

= k

and

(

)

= P

(

)

(

)

≡ F



,Γ

; R



= F

(

)

(59.121)

for vibrational or free states, respectively, and V

(

)

is the potential energy of state Λ

. Free–free transitions

always contribute to the line proﬁle, but bound-free and

free-bound transitions only contribute on the red and

blue wings, respectively. On using (59.82), (59.99), and

(59.109),

∆ω = ε

−ε

,andε

becomes the energy of

bound state j with vibrational quantum number v

when

< 0 . If



Γ, ε

,ε



≡



∞



∗

(

)

∆

(

)

(

)



(59.122)

[cf. (59.107)], where

∆

(

)

=−q



∗

(

r; R

)

r ψ

(

r; R

)

(59.123)

is the dipole moment, then using (59.119)), the free–free

contribution is given by

(

)



(

)

∞



f(v)

dv G(Γ, ε

,ε

(59.124)

where ε

µv

,andu

is the relative weight of

state Λ

[cf. Eqs. (59.106)–(59.108)]. The bound-free

contribution is

(

)



(

)



(

)



Γ, ε

,ε



(59.125)

and the free–bound contribution is

(

)



(

)

exp



−

∆ω











Γ, ε

,ε



(59.126)

where

g(ε) = 2π





f(v)

= 8π







2πk



3/2

exp



−



(59.127)

on using (59.21) with ε =

µv

. The full line proﬁle is

then given by (59.124)–(59.126), so that

(

)



j=0

(

)

(59.128)

The satellite features that are often seen in line wings

arise because turning points in the difference potential



(

)

−V

(

)



produce a phenomenon analogous

to the formation of rainbows in scattering theory. The

JWKB approximation is often used for the functions

(

)

, and can be shown to lead to the correct

static limit in which transitions take place at ﬁxed

values of R called ‘Condon points’, i.e., the Franck–

Condon principle is valid. Further details are given

in [59.9,10, 24–26].

Part D 59.5

888 Part D Scattering Theory

59.6 Uniﬁed Theories and Conclusions

The pressure broadening of spectral lines is in general

a time-dependent many-body problem and as such can-

not be solved exactly. After all, even the problem of two

free electrons scattered by a proton is still a subject of

active research. There is no practical theory that leads to

the full static proﬁle in the limit of high density (or low

temperature) and to the full impact proﬁle in the limit

of low density (or high temperature). As with so many

problems in physics, it is the intermediate problem that is

intractable because no particular feature can be singled

out as providing a weak perturbation on a known phys-

ical situation. However, much progress has been made

over the last thirty years in developing theories that take

into account many of the key features of the intermedi-

ate problem and they are often successful in predicting

line proﬁles for practical applications [59.8–10, 24–26].

More recently, time-dependent many-body problems

have been tackled using computer-oriented approaches

that invoke Monte Carlo and other simulation meth-

ods to study line broadening in dense, high-temperature

plasmas, see for example [59.27]. In this chapter, the

emphasis has been on aspects of the subject that relate

directly to electron-atom and low-energy atom–atom

scattering. Many experts in the ﬁelds of electron–atom

and atom–atom collisions are still not exploiting the di-

rect applicability of their work to line broadening. It

is hoped that this contribution will encourage more re-

search workers to study these fascinating problems that

not only provide links with plasma physics and in par-

ticular with the physics of fusion plasmas, but also with

a quite distinct body of laboratory-based experimental

data.

References

59.1 J. R. Fuhr, W. L. Wiese, L. J. Roszman: Bibliogra-

phy on Atomic Line Shapes and Shifts, Special

Publication 366 (National Bureau of Standards,

Washington, DC. 1972)

59.2 J. R. Fuhr, L. J. Roszman, W. L. Wiese: Bibliogra-

phy on Atomic Line Shapes and Shifts, Special

Publication 366 (National Bureau of Standards,

Washington, DC. 1974), Supplement 1

59.3 J. R. Fuhr, G. A. Martin, B. J. Specht: Bibliogra-

phy on Atomic Line Shapes and Shifts, Special

Publication 366 (National Bureau of Standards,

Washington, DC. 1974), Supplement 2

59.4 J. R. Fuhr, B. M. Miller, G. A. Martin: Bibliogra-

phy on Atomic Line Shapes and Shifts, Special

Publication 366 (National Bureau of Standards,

Washington, DC. 1978), Supplement 3

59.5 J. R. Fuhr, A. Lesage: Bibliography on Atomic

Line Shapes and Shifts, Special Publication 366

(National Institute of Standards and Technology,

Washington, DC. 1992), Supplement 4

59.6 A.Lesage,J.R.Fuhr:Bibliography on Atomic Line

Shapes and Shifts (Observatoire de Paris, Meudon

1998), Supplement 5

59.7 http://www.physics.nist.gov/PhysRefData

</Redirect/www.physics.nist.gov/PhysRefData>

59.8 H. R. Griem: Spectral Line Broadening in Plasmas

(Academic, New York 1974)

59.9 G. Peach: Adv. Phys. 30,367(1981)

59.10 N. Allard, J. R. Kielkopf: Rev. Mod. Phys. 54, 1103

(1982)

59.11 A. Ben-Reuven: Phys. Rev. 145, 7 (1966)

59.12 A. Ben-Reuven: Adv. Atom. Molec. Phys. 5,201

(1969)

59.13 R. Ciuryto, A. S. Pine: J. Quant. Spectrosc. Radiat.

Transfer 67, 375 (2000)

59.14 E. L. Lewis: Phys. Rep. 58,1(1980)

59.15 S. Sahal-Bréchot: Astron. & Astrophys. 1, 91 (1969)

59.16 S. Sahal-Bréchot: Astron. & Astrophys. 2, 322 (1969)

59.17 M. S. Dimitrijevi

c, N. Konjevi

c: J. Quant. Spectrosc.

Radiat. Transfer 24,451(1980)

59.18 N. Konjevi

c: Phys. Rep. 316, 339 (1999)

59.19 G. K. Oertel, L. P. Shomo: Astrophys. J. Suppl. 16,175

(1969)

59.20 M. J. Seaton: J. Phys. B 21, 3033 (1988)

59.21 M. J. Seaton: J. Phys. B 22, 3603 (1989)

59.22 V. I. Kogan, V. S. Lisitsa, G. V. Sholin: Rev. Plasma

Phys. 13,261(1987)

59.23 P. J. Leo, G. Peach, I. B. Whittingham: J. Phys. B 28,

591 (1995)

59.24 J. Szudy, W. E. Baylis: J. Quant. Spectrosc. Radiat.

Transfer 15,641(1975)

59.25 J. Szudy, W. E. Baylis: J. Quant. Spectrosc. Radiat.

Transfer 17, 269 (1977)

59.26 J. Szudy, W. E. Baylis: Phys. Rep. 266, 127 (1996)

59.27 A. Calisti, L. Godbert, R. Stamm, B. Talin: J. Quant.

Spectrosc. Radiat. Transfer 51, 59 (1994)

Part D 59

889

Scattering

Part E

Part E Scattering Experiments

60 Photodetachment

David J. Pegg, Knoxville, USA

61 Photon–Atom Interactions: Low Energy

Denise Caldwell, Arlington, USA

Manfred O. Krause, Oak Ridge, USA

62 Photon–Atom Interactions:

Intermediate Energies

Bernd Crasemann, Eugene, USA

63 Electron–Atom and Electron–Molecule Collisions

Sandor Trajmar, Redwood City, USA

William J. McConkey, Windsor, Canada

Isik Kanik, Pasadena, USA

64 Ion–Atom Scattering Experiments:

Low Energy

Ronald Phaneuf, Reno, USA

65 Ion–Atom Collisions – High Energy

Lew Cocke, Manhattan, USA

Michael Schulz, Rolla, USA

66 Reactive Scattering

Arthur G. Suits, Stony Brook, USA

Yuan T. Lee, Taipei, Taiwan

67 Ion–Molecule Reactions

James M. Farrar, Rochester, USA

891

Photodetachm

60. Photodetachment

Investigations of photon-ion interactions have

grown rapidly over the past few decades due

primarily to the increased availability of laser

and synchrotron light sources. At photon ener-

gies below about 1 keV the dominant radiative

process is the electric dipole induced pho-

toelectric effect. In the gaseous phase the

photoelectric effect is referred to as either

photoionization (atoms and positive ions) or

photodetachment (negative ions). This chapter

reviews developments in the ﬁeld of pho-

todetachment that have taken place over the

past decade. The focus will be on accelerator-

based investigations of the photodetachment

of atomic negative ions. The monographs of

Massey [60.1]andSmirnov [60.2] offer a good

introduction to the subject of negative ions.

Recentreviewsofnegativeionsandpho-

todetachment include those of Bates [60.3],

Buckman and Clark [60.4], Blondel [60.5], An-

60.1 Negative Ions ...................................... 891

60.2 Photodetachment................................ 892

60.2.1 Threshold Behavior ................... 892

60.2.2 Resonance Structure .................. 892

60.2.3 Higher Order Processes............... 893

60.3 Experimental Procedures...................... 893

60.3.1 Production of Negative Ions........ 893

60.3.2 Interacting Beams ..................... 893

60.3.3 Light Sources ............................ 894

60.3.4 Detection Schemes .................... 895

60.4 Results ............................................... 895

60.4.1 Threshold Measurements ........... 895

60.4.2 Resonance Parameters............... 896

60.4.3 Lifetimes of Metastable Negative

Ions......................................... 897

60.4.4 Multielectron Detachment .......... 898

References .................................................. 898

dersen [60.6], Andersen et al. [60.7]andBilodeau

and Haugen [60.8].

60.1 Negative Ions

Interest in negative ions stems from the fact that their

structure and dynamics are qualitatively different from

those of isoelectronic atoms and positive ions. This can

be traced to the nature of the force that binds the out-

ermost electron. In the case of atoms and positive ions,

the outermost electron moves asymptotically in the long

range Coulomb ﬁeld of the positively charged core.

The relatively strong 1/r potential is able to support

an inﬁnite spectrum of bound states that converge on

the ionization limit. In contrast, the outermost electron

in a negative ion experiences the short-range induced-

dipole ﬁeld of the atomic core. The relatively weak 1/r

polarization potential is shallow and typically can only

support a single bound state. The weakness of the bind-

ing is reﬂected in the magnitudes of electron afﬁnities

of atoms, which are numerically equal to the binding

energies of the outermost electron in the corresponding

negative ion. Electron afﬁnities are typically an order

of magnitude smaller than the ionization energies of

atoms. Excited bound states of negative ions are rare.

With the possible exception of Os

−

, all such states that

exist have the same conﬁguration, and therefore parity,

as the ground state. A rich spectrum of unbound excited

states, however, are associated with most ions. These

discrete states are embedded in the continua lying above

the ﬁrst detachment limit.

Electron correlation plays an important role in de-

termining the structure and dynamics of many-electron

systems [60.9]. Weakly bound systems such as neg-

ative ions are ideally suited for investigations of the

effects of correlation. As a result of the more efﬁ-

cient shielding of the nucleus by the atomic core, the

electron–electron interactions become relatively more

important than the electron-nucleus interaction in neg-

ative ions. The goal of photodetachment experiments

is to measure, in high resolution, correlation-sensitive

quantities such as electron afﬁnities and the ener-

gies and widths of resonant states. These quantities

Part E 60

892 Part E Scattering Experiment

provide sensitive tests of the ability of theorists to in-

corporate electron correlation into their calculations.

The stimulating interplay between experiment and

theory continues to help elucidate the role of many-

electron effects in the structure and dynamics of atomic

systems.

60.2 Photodetachment

Essentially all information about the structure and

dynamics of negative ions comes from controlled ex-

periments in which electrons are detached from the

ions when they interact with photons or other par-

ticles. Photodetachment is the preferred method of

studying negative ion structure and dynamics since

the energy resolution associated with such measure-

ments is typically much higher than that attainable

in any particle-induced detachment process. Generally,

one or more electrons are detached from a nega-

tive ion following the absorption of one or more

photons in the photodetachment process. Most measure-

ments to date, however, involve the simplest process

of single electron detachment following single pho-

ton absorption. Cross sections for this process start

at zero at threshold, rise to a maximum a few eV

above threshold and then decrease monotonically. Pho-

todetachment cross sections at their maximum have

a typical magnitude of ≈ 10–100 Mb. Threshold be-

havior and resonance structure in detachment cross

sections are of particular interest since they both

involve a high degree of correlation between the

electrons.

60.2.1 Threshold Behavior

Cross sections for photodetachment are zero at thresh-

old, in contrast to the ﬁnite value characteristic of

photoionization cross sections. The threshold behavior

is determined by the dynamics of two particles in the

ﬁnal continuum state. The Wigner law [60.10] governs

the energy dependence of the near-threshold cross sec-

tion for the photodetachment of a single electron from

an atomic negative ion. The Wigner law can be written

σ = Ak

2l+1

= B(E − E

)

l+1/2

, (60.1)

where k represents the wavenumber of the detached

electron, (E − E

) is the excess energy of the elec-

tron above threshold and l is the smallest value of

the orbital angular momentum quantum number. As

a result of the electric dipole selection rules, the de-

tached electron is represented, in general, by two

partial waves with l = l

+ 1andl

− 1, where l

is the angular momentum of the bound electron in

the negative ion prior to detachment. Wigner demon-

strated that for a two-body ﬁnal state the near-threshold

cross section depends only on the dominant long-

range interaction between the two product particles.

In the case of photodetachment involving electrons

with l > 0, this contribution arises from the centrifugal

force. Shorter-range interactions, such as the polariza-

tion force, will not change the form of the threshold

behavior but they will limit the range of validity of

the Wigner law. There is no a priori way of deter-

mining the range of validity of the Wigner law in

any particular experiment. It depends on the strengths

of short-range interactions. Measured threshold data

is usually ﬁt to the Wigner law in order to deter-

mine the threshold energy. In principle, it is possible

to extend the range of the ﬁt beyond that of the

Wigner law. O’Malley [60.11], for example, considered

the effects of multipole forces on threshold behavior.

O’Malley’s formalism, however, does not treat polar-

ization explicitly. This is, however, accounted for in

the modiﬁed effective range theory of Watanabe and

Greene [60.12]. Recently, Sandstroem et al. [60.13]

have used a modiﬁed effective range theory to ﬁt pho-

todetachment data taken at excited state thresholds of

the alkali-metal atoms, Li and K. In these cases the

dipole polarizability is very high and consequently the

range of validity of the Wigner law is correspondingly

small.

60.2.2 Resonance Structure

Negative ion resonances correspond to states in which

an electron and an atom are transiently associated.

Such states are the subject of a review by Buckman

and Clark [60.4]. In photodetachment they arise when

more than one electron, or a core electron, is excited.

These unbound discrete states are embedded in the con-

tinua above the ﬁrst detachment limit and are therefore

subject to decay via the spontaneous process of au-

todetachment. The allowed autodetachment process is

induced by the relatively strong electrostatic interaction

Part E 60.2

Photodetachment 60.3 Experimental Procedures 893

between the outermost electrons. This process causes

discrete continuum states to be very short lived. If the

selection rules on the allowed Coulomb-induced autode-

tachment process are violated, however, the state may

live much longer. Metastable states eventually decay

via autodetachment processes induced by the weaker

magnetic interactions. The He

−

ion is the prototypical

metastable negative ion. It is formed in the spin-aligned

1s2s2p

state when an electron attaches itself to

a He atom in the metastable 1s2s

S . It is bound by

77.516 meV [60.14]. The decay of a discrete state in the

continuum by autodetachment is manifested as a res-

onance structure in the detachment cross section. The

shape of a resonance is determined by the interference

between the two pathways for reaching the same ﬁnal

continuum state: direct detachment and detachment via

the discrete state embedded in the continuum. A reso-

nance can be parametrized by ﬁtting it to a Fano [60.15]

or Shore proﬁle [60.16]. The energy and width of

the discrete continuum state are extracted from the

ﬁt.

60.2.3 Higher Order Processes

With the advent of high power, pulsed lasers it became

possible to observe multiphoton detachment. In this pro-

cess a single electron is ejected following the absorption

of two or more photons. Early work in this area has

been reviewed by Crance [60.17], Davidson [60.18]and

Blondel [60.5]. More recently, Haugen and coworkers

have used two photon E1 transitions to determine ﬁne

structure splittings in the ground state of negative ions

and to measure the binding energies of excited states of

negative ions that have the same parity as the ground

state. Bilodeau and Haugen [60.8]havereviewedthese

measurements.

Multielectron detachment involves the detachment

of two or more electrons following the absorption of

a single photon. This process, which appears to be

initiated by the detachment of an inner shell electron,

requires photons with energies higher than can be gen-

erated by lasers. Such measurements can be performed

at synchrotron radiation sites.

60.3 Experimental Procedures

60.3.1 Production of Negative Ions

Negative ions are created in exoergic attachment pro-

cesses when an electron is captured by an atom or

molecule. These quantum systems are weakly bound

with diffuse outer orbitals. As a consequence, they are

easily destroyed in collisions with other particles. Due

to their fragility they are rarely observed in bulk matter.

The production of negative ions with a density sufﬁ-

ciently high for spectroscopic studies poses a challenge

to the experimentalist since processes involved in their

creation must compete with more probable destruction

processes. The most versatile source of production of

negative ions for accelerator-based experiments is the

Cs sputter ion source [60.19]. This source has been used

to generate a wide variety of atomic, molecular, and

cluster negative ions.

Negative ions can be produced and maintained in

ion traps [60.20]. In this case, the ions are produced

inside the trap by electron-induced dissociative attach-

ment collisions and photodetachment is investigated

by monitoring the depletion of the negative ions. The

most commonly used source for spectroscopic studies

of negative ions is, however, a beam produced by an

accelerator. In an accelerator-based apparatus the ions

are extracted from the ion source and focused to form

a collimated beam that is accelerated to a desired en-

ergy, typically 1–10 keV. Mass analysis of the ions is

used to produce an elementally and isotopically pure

beam that is essentially mono–energetic and unidirec-

tional. The directed particles then drift to the interaction

region through a beam line that is maintained at low

pressure to minimize destructive collisions between the

ions and the residual gas. Recently, negative ions have

been injected into storage rings. In this case the ions

make repeated passes through the interaction region.

The enhanced luminosity associated with multiple-pass

experiments makes it possible to investigate relatively

rare processes that would be impossible in single-pass

experiments.

60.3.2 Interacting Beams

The well-deﬁned spatial dimensions of an ion beam

readily permit an efﬁcient overlap with a beam of pho-

tons. The two interacting beams are most often mated in

either crossed or collinear beam geometries. The choice

of geometry is typically determined by the types of par-

ticles to be detected, the detection geometry to be used,

and the level of sensitivity and resolution required in

Part E 60.3

894 Part E Scattering Experiment

the experiment. The crossed beam arrangement is best

suited for spectroscopic studies of the photoelectrons

ejected following photodetachment, since the electrons

can most easily be collected from a spatially well deﬁned

interaction region. In a collinear beam arrangement it is

better to detect the residual heavy particles produced

in the photodetachment process since they all travel in

the same direction, the direction of motion of the ion

beam, and can be collected with high efﬁciency. Both

the sensitivity and energy resolution attainable using

a collinear beam apparatus are typically much higher

than for a crossed beam apparatus. Nowadays, most

experiments employ an apparatus in which the photon

and ions are collinearly merged and the present chap-

ter will focus on this arrangement. Figure 60.1 shows

a typical collinear beam apparatus that was designed

by Hanstorp [60.21]. The signal is enhanced when the

photon and ion beams are collinearly merged due to

the extended interaction region and the high collection

and detection efﬁciencies of the heavy residual par-

ticles. The major source of background noise in collinear

beam experiments is associated with the production of

atoms or positive ions by collisions of the beam ions

with the atoms or molecules of the residual gas in the

vacuum chamber. By maintaining a high vacuum, typic-

ally 10

−9

mTorr or better, one can keep the background

contribution to a tolerable level. In interacting beam ex-

periments involving the detection of the heavy residual

particles, the energy resolution that is attainable is usu-

ally limited by kinematic broadening. The amount of

broadening is determined by the properties of the ion

and photon beams and how they are overlapped. The

longitudinal velocity distribution of the ions in a beam

is compressed when the ions undergo acceleration af-

ter leaving the ion source [60.22]. If the photon beam

is merged collinearly with the “cooled” ion beam, the

photons sample the narrowed velocity distribution, thus

signiﬁcantly reducing the contribution from Doppler

broadening. If kinematic broadening is rendered neg-

ligible, the energy resolution is usually determined by

the bandwidth of the light source.

60.3.3 Light Sources

Since the particle density in the ion beam is typically

low, it is important to have a light source that gen-

erates an intense beam of photons. In addition, the

output of the light source must be tunable. Pulsed lasers

are most often used in photodetachment experiments.

Their time structure is often used to advantage in time-

of-ﬂight schemes to enhance the signal-to-background

Quadrupole

deflector

Ion

optics

Wien

filter

Ion

source

 3 mm

Interaction

region

 3 mm

Field

ionizer

Faraday cup

Positive

ion

detector

1, 2

2, 1

–

Fig. 60.1 A schematic of a collinear laser-negative ion

beam apparatus. The quadrupole deﬂector is used to merge

the laser and ion beam in the interaction region. The ﬁrst

laser is used to photodetach electrons from the ions. A sec-

ond laser beam is directed along the common path of the ﬁrst

laser beam and the ion beam. This laser is used in the state-

selective detection scheme based on resonance ionization.

The positive ions produced in the sequential interaction of

the negative ions with both laser beams and the external

electric ﬁeld are detected in a channel electron multiplier.

The directions of the laser beams can be reversed

ratio. The large peak powers characteristic of pulsed

lasers are required in multiphoton experiments. Lasers

or laser-based sources used in photodetachment experi-

ments span the wavelength range from the ultraviolet

to the infrared. Second harmonic generation in a non-

linear crystal is the conventional method of producing

UV radiation. The generation of tunable infrared ra-

diation with wavelengths of a few µm has proven

to be more difﬁcult. Recently, however, Haugen and

coworkers have performed experiments using infrared

radiation produced in a laser-pumped Raman conversion

cell [60.8]. Commercial optical parametric oscillators

are also becoming more readily available. In order to

investigate inner shell excitation and detachment pro-

Part E 60.3

Photodetachment 60.4 Results 895

cesses it is necessary to access the VUV or X-ray

region. These regions are currently outside the limits of

lasers and can only be accessed at synchrotron radiation

facilities.

60.3.4 Detection Schemes

Photodetachment events can be monitored by either

measuring the attenuation of the negative ions or by de-

tecting the particles (electrons, atoms or positive ions)

produced in the breakup of the ion. In accelerator-based

measurements the ion beam is too tenuous to be able to

monitor attenuation and particle detection must be em-

ployed. The heavy residual particles, atoms or positive

ions, are usually detected in experiments that employ

collinearly merged beams of photons and negative ions.

The selectivity and sensitivity of a measurement is

improved signiﬁcantly if the residual particles are state-

selectively detected. In the case of residual excited

atoms, the method most often employed is based on

the use of a second laser to excite the atoms to a state

near the ionization limit. This resonance step is followed

by electric ﬁeld ionization. The resulting positive ions

constitute the signal.

60.4 Results

There have been several new developments in ac-

celerator-based photodetachment measurements during

the past decade. Tunable infrared radiation has been

used in single photon and multiphoton experiments.

State-selective detection schemes based on resonance

ionization have been successfully employed in meas-

urements of thresholds and resonances. The lifetimes of

long-lived negative ions have been determined by the use

of magnetic storage rings. Synchrotron radiation sources

have been instrumental in the pioneering studies of inner

shell processes in negative ions.

60.4.1 Threshold Measurements

A measurement of a threshold energy using photode-

tachment allows one to determine the binding energy of

the extra electron in the negative ion or, equivalently, the

electron afﬁnity of the parent atom. Andersenet al. [60.7]

have recently published a review of the methods cur-

rently used to measure the binding energies of atomic

negative ions. The article includes an up-to-date compi-

lation of recommended electron afﬁnities. The simplest,

and potentially the most accurate, method of deter-

mining binding energies is the laser photodetachment

threshold (LPT) method. In this technique, the normal-

ized yield of residual atoms is recorded as a function

of the photon energy in the near-threshold region of the

cross section. In most cases, the Wigner law can be ﬁt-

ted to the data and the threshold energy is determined by

extrapolation. The Wigner law demonstrates that not all

thresholds have the same energy dependence. The most

accurate measurements to date involve detachment into

an s-wave continuum. In the case of l = 0, the thresh-

old energy dependence of E

1/2

is more pronounced

than for cases with l > 0. S-wave photodetachment re-

quires that a p-orbital electron be ejected. Haugen and

coworkers have used tunable infrared spectroscopy to

measure the binding energies of negative ions with open

p-shells [60.23–25]. In these experiments the detach-

ment process left the residual atom in its ground state so

that state-selective detection was not needed.

Considerable experimental and theoretical effort

have gone into investigating the negative ions of

the alkaline earth elements since the experimental

discovery [60.26] and subsequent theoretical conﬁrma-

tion [60.27]oftheexistenceofastableCa

−

ion in

1987. Prior to this time it was generally accepted that

the closed s-shell conﬁgurations of the alkaline earth

atoms would inhibit the production of stable negative

ions. Andersen et al. [60.28] have reviewed progress in

this ﬁeld. Andersen and coworkers used the LPT method

combined with state-selective detection to determine the

binding energies of the negative ions of the heavier al-

kaline earths Ca

−

, Sr

−

and Ba

−

[60.29–31]. No stable

negative ions of Be and Mg have been found, but the

−

ion is known to be metastable. These heavier ions

are weakly bound but tunable infrared sources were not

available at the time to detach them into the ground state

of the parent atom. Instead, UV radiation was used to

access an excited state threshold. In the case of Ca

−

the

4s5s

S threshold was used since it allowed access to an

s-wave continuum. In order to suppress the background

noise in the experiment, the Ca atoms left in this excited

state following detachment were selectively detected by

a method based on resonance ionization. Before the ex-

cited Ca atom could radiatively decay, a second laser was

used to induce a transition from the excited state to a high

lying Rydberg state. The Rydberg atoms were efﬁciently

Part E 60.4

896 Part E Scattering Experiment

ionized in an electrostatic ﬁeld applied to the beam. The

ion thus produced were used as the signal that, once

normalized, was proportional to the photodetachment

cross section. The structures of the heavy alkaline earths

are very difﬁcult to calculate. Three relatively loosely

bound electrons move in the ﬁeld of a highly polarizable

core. Electron correlation and relativistic effects must be

included in a theoretical description of their structure.

As calculations became more sophisticated it became

clear that correlations between the core electrons and

between the valence and core electrons had to be taken

into account in addition to the correlations between the

valence electrons [60.32].

The negative ions of the alkali-metal elements have

a closed s-shell conﬁguration. In this case it is nec-

essary to access an excited state threshold in order

to detach into an s-wave continuum. Hanstorp and

coworkers have used the LPT method combined with

state-selective detection to measure the electron afﬁni-

ties of Li [60.33] and K [60.34]. Since accelerator-based

measurements involve the use of fast and unidirectional

beams of ions, one must take into account Doppler

shifts in accurate measurements of threshold energies.

In the K

−

experiment [60.34], two separate sets of

data were accumulated, one with the laser and ion

beams co-propagating and the other with them counter-

propagating. The Doppler shift can be eliminated to all

orders by taking the geometric mean of the measured

red-shifted and blue-shifted threshold energies [60.35].

LPT measurements can be used to selectively sup-

press one isotope relative to other isotopes of the same

element, thereby changing the relative abundances from

their natural values. This technique could be applied,

for example, to the problem of sensitivity enhancement

in mass spectrometry by suppressing unwanted isotopic

interferences. Sandstroem et al. [60.36] recently per-

formed a proof-of-principle experiment using the

and

S isotopes. The goal of the experiment was to en-

rich the

S isotope relative to the more abundant

isotope. Due to the large differential Doppler shifts as-

sociated with the fast moving ions of the two isotopes

of different masses, it was possible to selectively pho-

todetach one isotope and leave the other untouched. In

this feasibility experiment, the

S ration was en-

hanced by a factor of > 50 over its natural value. With

a better vacuum and the selection of a more suitable

laser, it is predicted that the enhancement ratio could be

signiﬁcantly improved. The application of LPT to mass

spectrometry clearly has the potential for enhancing the

sensitivity in measurements of the abundances of rare

and ultra-rare isotopes.

60.4.2 Resonance Parameters

The simplest negative ion is the two-electron H

−

ion.

This three-body Coulomb system is fundamentally im-

portant in our understanding of the role played by

electron correlation in atomic structure. The pioneering

measurements of the photodetachment of one and two

electrons from the H

−

ion were performed by Bryant

and coworkers [60.37–39] several decades ago. The

ASTRID (Aarhus storage ring Denmark) heavy ion stor-

age ring has been used in two new measurements of

the resonance structure in the vicinity of the H(n = 2)

threshold [60.40, 41]. The energy resolution of these

storage ring experiments was much higher than that

attained in previous experiments. As a consequence, An-

dersen et al. [60.41] were able to observe, for the ﬁrst

time, a second resonance below the H(n = 2) threshold.

In principle, the 1/r

dipolar potential should support

an inﬁnite series of resonances below each excited state

of the H atom [60.42]. Calculations, however, indicate

that the series will be truncated after the third member

by relativistic and radiative interactions [60.43].

Detachment continua contain a wealth of structure

and many measurements of Feshbach resonances in

non-hydrogenic negative ions have been reported dur-

ing the past decade. The dipole polarizability of an

atom increases with the degree of excitation, making

it easier for electrons to attach to the excited parent

atom. Series of Feshbach resonances containing several

members are often found below excited state thresh-

olds. Resonances in the photodetachment spectra of

the metastable He

−

ion [60.44] and the alkali-metal

negative ions [60.45–49] have been studied exten-

sively by Hanstorp and coworkers using the collinear

beam apparatus shown in Fig. 60.1. R-matrix calcu-

lations [60.50–53] have generally been successful in

predicting the energies and widths of most of the res-

onances observed in the experiments. There has been

keen interest in the similarities and differences between

the photodetachment spectra of Li

−

and H

−

The He

−

ion is a metastable negative ion but it

is sufﬁciently long lived to pass from the ion source

to the interaction region with relatively little attenua-

tion via autodetachment. Electric dipole selection rules

limit photon-induced transitions from the 1s2s2p

ground state to excited states with

Pand

Dsym-

metry. The spectra of Feshbach resonances that lie

below the He(n = 3, 4, 5) thresholds have been inves-

tigated using the collinear beam apparatus shown in

Fig. 60.1 [60.44,54, 55]. Resonance ionization was used

to state selectively detect the residual excited He atoms.

Part E 60.4

Photodetachment 60.4 Results 897

Figure 60.2 shows a high resolution spectrum of the res-

onance structure in the range 3.7–4.0 eV, a range that

encompasses the H(n = 4) thresholds. In this relatively

small energy range Kiyan et al. [60.44] found many res-

onances exhibiting a variety of different shapes. The

resonances labeled a,c,e are members of the

Pseries

with dominant conﬁgurations of 1s4pnp(n = 4, 5, 6).

The resonances labeled b,d appear to be the n = 5, 6

members of the 1s4sns

Sseries.

Recent studies using synchrotron radiation have re-

vealed resonances in photodetachment cross sections

in the X-ray and VUV regions that can be associated

with the excitation of inner shell electrons. Resonances

arising from K-shell excitation in the Li

−

ion have

been reported by Kjeldsen et al. [60.56]andBerrah

et al. [60.57]. Similarly, resonances were found in

a study of He

−

[60.58]andC

−

[60.59]. Resonances

associated with L-shell excitation of the Na

−

ion were

observed by Covington et al. [60.60]. Figure 60.3 shows

3.75 3.80 3.85 3.90 3.95 4.00

Photon energy (eV)

Normalised He

signal

ab c d e f

3.95 3.96 3.97

Fig. 60.2 Partial cross section for the photodetachment of

−

via the He(1s3p

P)+e(kp) continuum channel in the

energy range 3.73–4.00 eV. The open circles represent the

measured data. The ﬁts to the sum of Shore proﬁles are

shownbythesolid lines. The energies of the resonances

obtained from the ﬁts are shown as short vertical lines.The

inset shows the region near the He(1s4p

P) threshold in

ﬁner detail

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

Cross section (Mb)

Photon energy (eV)

30 35 40 45 50

3s(

)4s

Fig. 60.3 Total cross section for the photodetachment of Na

−

over

the range 30–51 eV. Thresholds are indicated by vertical lines. The

peaks are resonances associated with the excitation of a 2p core elec-

tron accompanied, in most cases, by the excitation of a 3s valence

electron

part of the spectrum in which the dominant feature is

a resonance at ≈ 36 eV that arises from the excitation

of a pair of electrons – a 2p core electron and a 3s va-

lence electron. Absolute cross sections were measured

in most of the experiments. R-matrix calculations of

the cross sections at energies corresponding to K-shell

excitation have successfully accounted for most of the

observations [60.61–63].

60.4.3 Lifetimes of Metastable Negative

Ions

Heavy ion storage rings are well suited for studies

of the radiative or autodetaching decay of long lived

excited states of negative ions. They have also been

used to investigate the effect of blackbody radiation

on weakly bound stable negative ions [60.64]. Ander-

sen and coworkers have used the ASTRID facility to

measure the lifetimes of the metastable negative ions

−

[60.65]andHe

−

[60.66] against autodetaching de-

cay. The decay rate was measured by simply detecting

the neutral atoms produced in the ring as a function of

time after injection. The range of autodetaching life-

times that can be measured in a storage ring depends on

the size of the ring and on the destruction rate of the

ions by collisional detachment with the residual gas in

Part E 60.4