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Recent experimental achievements with negative ions

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1995 Phys. Scr. 1995 31

(http://iopscience.iop.org/1402-4896/1995/T58/004)

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Physica Scripta. Vol. T58, 31-42, 1995

Recent Experimental Achievements with Negative Ions C. Blonde1

Laboratoire Aime-Cotton, bltiment 505, F-91405 Orsay cedex, France

Received July 13,1994: accepted August 22,1994

Abstract Experimental results obtained about the atomic physics of negative ions since the Physica Scripta 1991 review are presented. Most new data concern the metastable states and resonances of He- and alkaline-earth negative ions, and the ions of the C- column. A few photodetachment experiments were also performed on ions submitted to external fields, and we have now a better understanding of the response of negative ions to microwaves and ponderomotive threshold shifting. A great progress was made in the study of multiphoton detachment processes; 1991 was the year of discovery of excess-photon detachment. Every year brings new precision detachment threshold measurements about, but still relying on the 1985 measurement numerical reasons make it necessary to revise the electron affinity ofoxygen: E A ( 0 ) = 11 784.648(6)cm-l, or 1.4611 107(17)eV.

1. Introduction 1.1. General features about negative ions

Negative ions have long been considered as “exotic” species, seldom used in actual atomic physics experiments, just appearing under the form of resonances in electron-atom collisions, but with no actual discrete states that would give way to real spectroscopic studies.

It has now been realized for some years that negative ions provide us with a very interesting field of experimentation and testing for a variety of atomic theories. On the other hand, they can be utilized as an alternative to neutral atoms in some situations where the role of the Coulomb field on the excited electron has to be elucidated.

An electron going through a - supposedly - frozen neutral atom undergoes a locally attractive potential as soon as it penetrates the outermost electronic shell, for the Coulomb attraction of the nucleus then ceases to be com- pletely shielded. Penetration of this extra electron to form a stationary state is however limited by the fact that the deeper orbitals are occupied. Even when the independent electron picture, the precise form of which is the Hartree- Fock model, succeeds at predicting a stable negative ion, it .only produces a gross figure of the ion’s stability. For instance Hartree-Fock calculations [l] find less than one half of the attachment energy of F-.

Negative ions thus owe an essential part of their stability to electron correlations. Electron correlations are present as soon as one can no longer consider that the motion of an electron only depends on the average position of the other ones. In other words, electron correlations are the way elec- trons share the attraction of the nucleus, and this of course has the effect of increasing the stability of the ion.

This stability is measured by the energy necessary to remove an electron from the negative ion, i.e. to neutralize, or to “detach” it. It is, conversely, the electron affinity of the neutral atom. Comparing calculated electron affinities with the measured ones is conceptually the simplest test of the

ability of existing methods to properly model electron corre- lations. Actually, the best known electron affinities, the mea- surement of which will be described in Chapter 2, are generally far ahead of the precision of calculations.

Because exciting the outer electron brings it to move around a neutral core, no Rydberg series can exist in a negative ion. Most negative ions do not even have any other stable discrete level than their ground level, and excited dis- crete states often only appear as resonances embedded in the photodetachment continuum. Chapter 3 will be devoted to a description of typical examples of such resonances, again taking into account, as an essential criterion, the degree of electron correlation that characterizes the corre- sponding states. With Chapter 4, we will enter the regime in which negative ions interact with external fields, either static (electric or magnetic) or oscillatory. Chapter 5 will describe the response of negative ions to intense fields, and what they have taught us about multiphoton processes.

1.2. The scope of the present article A review about the spectroscopy of negative ions was already presented at the EGAS conference in Uppsala [2]. Another review very recently appeared about “Atomic negative-ion resonances” [3].

The present article will first aim at giving a pedagogical description of the atomic physics of negative ions, with selected examples. A good part of Andersen’s review [2] was devoted to molecular negative ions. We will instead give some insight into the high-field effects on negative ions.

Buckman and Clark’s review [3] gives a very complete description of theoretical methods and takes most of its experimental background from collision experiments. We will instead adopt a spectroscopist’s point of view, and focus on the most recent experimental results that were not included in these previous reviews.

1.3. The main diferences between negative ions and neutral atoms The difference between a neutral atom and a negative ion is beautifully illustrated by the calculated spectrum of the oscillator strengths for exciting hydrogen from its ground state into the n, EP channel (Fig. 1 ) [4]. Exciting an atom to higher and higher energies always brings infinite series of discrete levels about, the so-called “Rydberg series”, that converge to the ionisation threshold.

A photoionisation cross-section at threshold is always equal to the limit of the photoexcitation cross-section of the corresponding Rydberg series (once averaged over the energy interval of adjacent levels). Since actual experiments always have finite spectral resolution, and since, because of stray electric fields, ionisation always begins below the

Physica Scripta T58

32 C. Blondel

-6 - 5 - 4 -3 -2 -I 0 I 2 3 4 5 Elev,

Fig. 1 . The spectral density of atomic oscillator strength, from the ground state of atomic hydrogen. Because it continues Rydberg series excitation, photoionisation has a finite value at threshold. Reprinted with permission from [4], @ 1968 The American Physical Society.

unperturbed threshold there is no way for a direct observ- ation of the photoionisation threshold of a neutral atom.

On the contrary, in negative ions absence of the Rydberg series has the consequence that the photoexcitation cross- section necessarily starts from zero at threshold. This is the reason why, in contradistinction to the theoretical spectrum of Fig. 1, the general features of a photodetachment thresh- old can be illustrated by a real, experimental spectrum (Fig. 2) [ 5 ] . The apparent onset of detachment really indicates where the threshold is.

Because the presence of the neutral core perturbs the motion of the outgoing electron only in a limited volume, the final state of the photodetached electron can be con- sidered as the one of a free-electron, the wave-function of which is a plane-wave. This "plane-wave'' or "free-electron'' approximation leads to a very general behaviour of the detachment cross-sections at threshold; 1 being the orbital angular momentum of the outgoing electron, E its kinetic energy, the partial cross-section cl(&) varies as 8'' l'' (Wigner law) [SI.

This law has two consequences. First it shows precisely that every partial cross-section, hence the total detachment cross-section, starts from zero at threshold. Secondly, the dependence of the exponent on 1 is such that threshold detachment necessarily yields electrons of the lowest angular momentum allowed by the selection rules, and that the branching ratio to higher angular momenta rapidly increases when the energy E increases above threshold. This again is to be compared to ionisation of a neutral atom,

1000 1 - 2 - 5 5 0 0 1 - C m - U) .-

0- , l l , , , l l l l , , l # t , , l

' 27128.5 27129.0 27129.5 27130.0

-

photon energy (cm-'1 Fig. 2. Photodetachment of Br- at threshold [SI. Were it not for the finite resolution of the laser and hyperfine structure of neutral Br, the derivative of the cross-section would be infinite at threshold.

Physica Scripta T58

where the series of angular momentum channels also open in a progressive way, because the outgoing electron also has to overcome the centrifugal barrier, but this takes place in the discrete part of the spectrum. The equivalent of the Wigner power law for an atom is that an 1-state does not exist unless the principal quantum number n is at least 1 + 1. Finally, of course, all angular momentum channels are open when one reaches the ionisation threshold.

A practical advantage of the Wigner law is that when photodetachment takes place with an even state as the final state, photodetachment at threshold shall start with an infinite derivative (as A). This makes the onset of detach- ment sudden and conspicuous. Photodetaching the negative ion under study with a tunable laser has become the stan- dard method for measuring electron affinities.

2. Precision electron affinity measurements 2.1. T h e electron affinity of hydrogen

The electron affinity of hydrogen has been for long an exception in the sense that it was better known by calcu- lation [7, 81 than from experimental measurement. We now at last have an experimental determination of the detach- ment threshold of H- that can compete with the precision of ab initio calculations.

The electron affinity of hydrogen is 6082.99(15)cm-' or 0.754 195(19)eV [SI. The laser used to probe the infrared threshold excitation was a specially constructed F-center laser, with a tuning range from 1.45 to 1.75 pm. To properly define the threshold, one has to have in mind that it corre- sponds to leaving the neutral atom in its lowest hyperfine sublevel, which is also the one with the smaller statistical weight. An additional difficulty is due to the fact that both H and H- have even-parity ground states, which implies that the dominant one-photon detachment channel at threshold is the p-channel. The detachment cross-section thus starts with zero derivative at threshold, which makes the fitting procedure a little less precise than for s-wave detachment. These difficulties explain why the experiment only achieved a precision of 25ppm, not enough to dis- tinguish between the two calculations [7, 81. Figure 3 shows the onset of photodetachment at threshold when the col-

6095 6097 6099 PHOTON ENERGY (cm-1) 6 'o '

Fig. 3. Photodetachment threshold of H- with laser and ion copropagat- ing beams. The electron taken from an even orbital here detaches into a p-wave, hence a zero slope at threshold. Reprinted with permission from [SI, @ 1991 The American Physical Society.

Recent Experimental Achievements with Negative Ions 33

CA Y C a 0 U

400 - 5 1 3 0 0

200

100

0

405 .20 405 .21 405 .22 Wavelength (nm)

Fig. 4. Photodetachment threshold of I - . The hyperfine structure of neutral iodine makes it a succession of four thresholds. Reprinted with per- mission from [16], 0 1992 I O P Publishing Ltd and the authors.

This result has also been translated into eV, but the 1986 adjustment of the physical constants [14] comprised a sig- nificant revision of the eV/(cm- ') conversion factor, for we now have 8065.5410(24) cm- '/eV. After revision, the elec- tron affinity of oxygen is 1.4611 107(17)eV. Still more than one half of its relative uncertainty comes from converting cm-' into eV. The relative precision of this measurement, which remains a record among all atomic electron affinities, is f 0.3 ppm (in cm- ').

Sulfur comes next, with a precision of f0 .6ppm [ls], but its electron affinity probably has to be slightly revised, also following the 1986 adjustment, to give now EA(S) = 2.077 104(3)eV.

More recent electron affinity measurements have concen- trated on the halogen negative ions. Br- and F- have had their photodetachment threshold measured with respective precisions of k0.6 and k 1.0ppm: EA(Br) = 27 129.170(15)cm-' and EA(F) = 27432.440(25)cm-' [SI. These results show that in spite of first-order Doppler broadening, transverse laser photodetachment threshold spectroscopy can achieve nearly as precise measurements as collinear spectroscopy. Care must be taken however of the impossibility of having perfectly orthogonal beams, which was circumvented by the use of a corner cube to send the laser perfectly parallel to itself back onto the ion beam. The arithmetical average of the two apparent thresholds record- ed in this way at least completely eliminates the first-order Doppler shift [SI.

Collinear spectroscopy was still used for iodine [16],

linear H - and laser beams were copropagating, as a func- tion of the photon energy. It suggests how difficult it can be to determine the detachment threshold of negative ions detaching into an odd wave at a GHz scale. More precise measurements seem to be necessary however, in order to understand the origin of the discrepancy between ab initio calculations [7, 81.

2.2. The light elements of Z > 2 Helium does not make a stable negative ion. Its most famous metastable states will be described in the next chapter.

The best-known electron affinity of all atoms remains the one of oxygen. It was measured in 1985 using a beam of 0- and a collinear tunable laser beam [lo].

The high velocity of an ion beam produces high Doppler shifts. Collinear spectroscopy even gives these shifts their extremum values, which has the advantage of eliminating first-order Doppler broadening due to angular dispersion either of the laser or of the ion beam. Moreover measuring the parallel and antiparallel Doppler-shifted wave-numbers of the threshold also makes it possible to correct for the Doppler effect at all orders without even knowing the veloc- ity of the ions [ll]. Indeed, with U the velocity of the ion beam, one can define the "rapidity" U by u/c = tanh (U). The frequency transformation from the ion frame to the labor- atory then just consists of a multiplication by e" or e - " for parallel or antiparallel beams, respectively. Since e-"e" = 1, the geometrical average of the apparent wavenumbers mea- sured for the two beam configurations automatically yields the unshifted photodetachment threshold.

Laser photodetachment spectroscopy of 0 - has given 11 792.376(6) and 11 776.925(6) cm- ' as the laboratory photodetachment thresholds for parallel and antiparallel beams, respectively [lo]. But the authors of the measure- ment did not use the geometrical method, and forgetting a power of 1/2 in the second-order Doppler correction factor [12] led them to a slight error of 0.003cm-' in the electron affinity of oxygen. The proper result should be [13]

E A ( 0 ) = 11 784.648 (6)cm-'.

the electron affinity of which was found to be 24 672.795(80) cm- ', with a precision of k 3 ppm, or 3.059038(10)eV. In this case as in the former, the detach- ment threshold is defined as the detachment energy to the lowest hyperfine structure level of the neutral atom, and the precision reached is now large enough so that one can nearly see the succession of hyperfine detachment thresholds due to this structure of, typically, a few GHz (Fig. 4).]

In order to make this review of the electron affinities of the halogen complete, let us mention that the best measure- ment still available for the detachment threshold of C1- still is the one by Trainham et al. [17], with EA(C1) = 29 138.3(5)cm-', i.e. 3.61 269(7)eV, with a precision of 18 ppm. The technique used was laser photodetachment at threshold of C1- ions contained in a Penning trap, which shows a possible alternative to the most intuitive ion beam technique. The electron affinity of chlorine is an important figure anyway, because it is the maximum electron affinity of all atoms. In other words, C1- is the most tightly bound of all atomic negative ions.

As for corresponding calculations, ab initio calculations of electron affinities are difficult, because they imply comparing the total binding energy of the neutral atom to the binding energy of the negative ion, i.e. determining a small quantity as the difference of two much larger ones. Noticeable effort has been devoted in the last few years to improve the calcu- lated electron affinities of the light atoms B, C, 0, F [l , 181 or the halogen [19]. Because it is the lightest ion, F- has been the common subject of these studies, but they still hardly reproduce the first two digits of the actual detach- ment energy of F- , thus showing how far electron affinity measurements generally lie ahead of electron affinity calcu- lations.

Physica Scripta T58

34 C. Blondel

3. Negative ion spectroscopy

In the present chapter, we will first describe “metastable states”, then “resonances”. Of course, both are fundamen- tally of the same nature, for they result from the coupling of a discrete state with the detachment continuum. We will consider as “metastable states” those with a lifetime large enough to make their presence detectable, e.g. along an ion beam. Metastable states can be used as relay states for step- wise excitation.

“Resonances” instead are the autodetaching states of so short a lifetime that they are only revealed by the structures they produce in the photodetachment, or collisional detach- ment spectra. Obviously, depending on the detection scheme used, metastable states can also appear as narrow detach- ment resonances.

3.1. Metastable states in alkaline-earths 3.1.1. H e - . Like all noble gases, helium does not form a stable negative ion. As stated by Pegg et al. [20] “He- is instead the prototype of an unusual class of unstable, yet long-lived negative ions that are metastable against decay via electron (autodetachment) and photon (electric dipole) emission”. Figure 5 shows an energy diagram of both the first energy levels of He and the metastable He-. Metastable He- appears at its “ground-state” energy as resulting from the exoenergetic capture of an electron by a ls2s3S1 He core to form a spin-aligned ls2s2p 4P term.

The existence of a bound discrete state just below an excited detachment threshold of the ion is the analogous of the autoionized Rydberg series that converge to every upper ionization threshold of an atom. But having autoionized discrete states with an electron bound to an excited ionic core is by no way extraordinary, for the Coulomb potential created by the core can always support infinite series of dis-

2p2 3P 2P3 %,, 481301 cm“

radiative autodetachment I autodetachment

159850 cm-’

He- U Is2 s, He

Fig. 5. First energy levels of He and metastable states of He-. When fine structure is not indicated, the average term energy is given. See references in text.

Physica Scripta T58

Crete Rydberg levels. On the contrary, in negative ions, the properties of the autodetaching levels very sensitively depend on the configuration of the core, and on the possi- bility it offers to have an extra electron trapped in a strongly correlated state.

The first metastable level of He- appears as a good case. The term ls2s2p4Po means that all three electrons, having different orbital states, can align their spins to give the maximum S = 3/2 total spin value. If L-S coupling was perfect, the ion would then be everlasting against autode- tachment, for it can only decay to a S = 1/2 continuum (ground state helium has zero total spin) and has no electric dipolar emission since it is the lowest energy state with such a total spin value.

In more details, the metastability of ls2s2p4P He- has been predicted to strongly depend on the fine structure state of the ion [21], for the spin-orbit and spin-spin interactions can mix its 4P1,2 and 4P3,2 states with and ’P3!2

states, respectively, while the 4Ps/2 states will lose their quartet character only though spin-spin interaction. In fact, 4Plj2, 4P3,2 and 4P5j2 autodetach with lifetimes of 16 & 4 [22], 12 5 2 and 350 ? 15ps [23], respectively, but the most recent calculations indicate that the 4Ps,, fine struc- ture level owes less of its outstanding stability to a purer S = 3/2 character than to the fact it has a decay by emitting an electron into anf state [24]. The transition amplitude to such a high angular momentum state is just smaller than to p waves, that serve as final states for autodetachment of the two lower4 fine structure levels.

If one really wants an electron affinity, despite the fact He- has no stable state, one can still measure the energy of the ls2s2p4Po term with respect to the “parent” ls2s3S1 state of the atom. The electron affinity so defined can be interpreted as the binding energy of the extra electron to the excited neutral core. Since this detachment energy is very low, it is more easily measured by a trick which is often used in this situation, which consists of measuring the threshold energy not of the first possible detachment process ls2s2p 4P0 He- + hv + ls2s 3S1 He + ES, but of the second one: ls2s2p4Po He- + hv + ls2p 3P0 He + EP. The “electron affinity” is then obtained just by subtracting the well-known transition energy of the neutral atom ls2s 3S1 - ls2p 3P“ to the measured energy of the second threshold, One finds in this way that metastable He- lies 77.5 f 0.8 meV below the ls2s 3S, state of neutral helium [25].

That many excited states of a neutral atom, like helium, can give birth to a metastable state of the corresponding ion by trapping an extra electron in a highly correlated state is already impressive of how symmetries and electron corre- lations can protect the atomic shell against autodetachment. Still more impressive is the fact that an autoionizing state of the neutral atom, here helium in its 2p2 3 S , state, can serve as a trap for an extra electron, provided it enters the same subshell as the other ones, to form a 2p3 4S3,2 triply excited negative ion! This level has proven to be stable enough to be detectable through its radiative autodetachment line [26]. Its lifetime, known only theoretically, would be 0.1 ns

3.1.2 B e - . Beryllium is very similar to helium in the sense that it does not form a stable negative ion, but its excited states can bind an extra electron to make spin-aligned meta- stable states of the negative ion. The first of these levels is

1271.

the which, as for the first metastable state of He-, essentially owes its metastability to the fact that its only autodetachment channel is to a S = 1/2 continuum (see Fig. 6 for an energy diagram).

Beryllium also provides us with the remarkable example of an optical transition between metastable states in a nega- tive ion. Optical spectroscopy following beam-foil inter- action (with very thin carbon foils) reveals the presence of spontaneous emission from the ls22p3 4S3,2 to the former ls22s2p2 4P metastable level [28]. This extraordinary line had already been shown at this conference in 1990 [2].

Since then, several groups have developed more studies of the Be- ion. The heavy-ion storage ring technique was used to measure the lifetimes of the fine-structure components of the ls22s2pZ4P level [29]. These lifetimes were found to be 0.25 k 0.15, 45 f 5 and 0.25 & 0.15 ps for J = 1/2, J = 312 and J = 512, respectively. The comparison with helium is very tentative, and one can be surprised that the most stable component of the 1 ~ ~ 2 s 2 p ~ ~ P metastable level is not the J = 512 one. However, the configuration that gives rise to this level is an even one, whereas the first metastable level of He- comes from an odd configuration. The autodetachment channels are thus completely different, as are the details of the coupling [24, 301. The relative stability of ls22s2p2 4P3,2

Be- actually appears as an accident, due to destructive interference between direct autodetachment of the 4P3,2 states into the continuum and indirect autodetachment due to 2L3,2 admixture in the doubly excited states. This acci- dental balance is not reproduced for the equivalent 3s3p2 4P states of Mg-, nor for the 4s4p2 4P states of Ca- [24].

Photodetached-electron spectroscopy has been used to determine the relative electron affinity of 2s2p 3P Be to form 2 ~ 2 p ~ ~ P Be-. It was found to be 261 f 10meV [31]. This is just 4.2meV less than the electron affinity of 2p2 3P Be to form 2p3 4S Be-, which proved enough to distinguish the ionic from the atomic line [28].

3.1.3. Other alkaline-earth negative ions, calcium. Neither Mg- nor Ca- were thought to form any long-lived

2 $ 3 p

59696 cm-’

2s 2p 3PS

21980 cm-‘

2s2 Is,

Be

2p3 %;, 57557 cm” i optical transition i n

Fig. 6. First energy levels and metastable states of Be-. The similarity of the 4P metastable term with the one of He- should not conceal the oppositeness of their parities.

Recent Experimental Achievements with Negative Ions 35

nsnp’ 4Pe metastable state [24], but in 1989 Hanstorp et al. [32] claimed to have formed 4 ~ 4 p ~ ~ P , , , Ca- by the clas- sical technique of double charge exchange in cesium vapor. Subsequent calculations showed however that the most stable fine structure level of 4 ~ 4 p ~ ~ P Ca- was more likely to be 4P1,2, but its calculated lifetime [30] remained three orders of magnitude smaller than the observed 290 f 10 ps.

Ca- also possesses a 4s24p2P0 stable ground state. Its detachment threshold had first been measured by photoelec- tron spectroscopy at 43 f 7 meV ,[[33], but other measure- ments in 1992 led to new and significantly reduced values: 18.4 & 2.5 [34] and 17.5”:meV [35]. This electron affinity is so small that blackbody radiation at not especially high temperatures is enough to detach ground state Ca- ions with an apparent lifetime in the 10-4s range [36]. That Ca- beams have contained metastable 4P Ca- remains sure however, but with a certainly much shorter lifetime [37]. A review of the different methods used to calculate the elec- tron affinity of calcium appeared recently [38].

3.2. Resonances 3.2.1. About the nature of resonances. Negative ion reso- nances were the subject of a comprehensive review very recently [3]. We shall thus give here only some general ideas, and illustrate them by a few examples.

Resonances in photodetachment or e--atom scattering are traditionally classified as Feshbach or shape resonances. Shape resonances arise from the possibility for the scattered or detached electron to be trapped transitorily by the poten- tial created by the neutral core, if this potential has a proper shape. This can be the case if the electron possesses angular momentum, for the l/r2 centrifugal term of the radial poten- tial will then create a barrier, that can produce reflection and trapping if the interference inside the barrier happens to be a constructive one. A shape resonance, which will then have a large spectral width, can even be produced above the barrier top. Shape resonances are essentially a one-electron phenomenon, and are naturally found at energies higher than the energy of the parent atom.

Feshbach states are instead states in which the excited electron remains bound for a long time (on the scale of atomic times) thanks to a reorganisation of the atomic core, especially if the atom finds an energetical advantage at giving room to an extra electron, which will then be absorbed in a high-correlated state of the outer shell. The detachment channels of a Feshbach resonance always imply taking some energy back from the atomic core to produce an outgoing electron of positive kinetic energy. Feshbach resonances are naturally found below the corresponding energy levels of the parent atom.

As stressed by Buckman and Clark [3], such a classi- fication is of course an idealisation. Trapping an additional electron never leaves the atomic core totally frozen and, on the other hand, reorganisation of the atomic shell to give room to an extra electron is never so complete that it becomes wholly different from the parent state of the atom. A deeper analysis of the nature of resonances often requires the use of special descriptions of the whole outer shell of the negative ion, such as hyperspherical coordinates in the case of H- [39], or even molecular coordinates as was done to investigate the curious positronium negative ion [40]. The hyperspherical point of view also proved to be very fruitful

Physica Scripta T58

36 C. Blondel

-

to classify the resonances of He-, which were found to exhibit interesting similarities to those of H - [41].

3.2.2. Hydrogen. Because it is the most elementary nega- tive ion, H- has been the subject of the greatest number of theoretical studies. From the experimental point of view however, studying H - is a difficult challenge. We have already described the electron affinity measurement of hydrogen, which required building a special laser system [9] to reach the detachment threshold at 0.754eV. To reach excited states, or resonances of H- one has to add, roughly, the excitation energy of the excited series of neutral H, 10.2 eV at least. References to collisional studies around this energy will be found in the review by Buckman and Clark [3]. Photoexcitation at such energies is noticeably more dif- ficult. Vacuum ultra-violet or multiphoton excitation is required, which explains that relatively few experiments were carried out. Photoexcitation has the advantage of a better identification of the final states, thanks to the selec- tion rules, but photodetachment from the ground state is blind to anything else than ‘P; resonances.

Photodetachment of H - could be achieved using a rela- tivistic beam of H - ions, which gives impressive possibilities of Doppler tuning. One Feshbach and the shape resonances near the n = 2 hydrogenic threshold were clearly observed [42] and have already been presented by Andersen [2]. The same part of the spectrum is reproduced by the calculation of Sadeghpour and Greene [39], which shows the corre- sponding rate for leaving the hydrogen atom in its n = 2 excited state (Fig. 7). The shape resonance induces a peak of n = 2 production, whereas the Feshbach states have to decay to the lower channel.

At higher energies, the resonances take the form of series of dips of the cross-section, that develop in the vicinity of every excited threshold. These resonances were observed near the n = 5 , 6, 7 and 8 thresholds E431 and qualitatively interpreted using Macek’s hyperspherical coordinates as having well-defined symmetry properties, in terms of corre- lated motion [39].

In a more elaborate experiment, the same group investi- gated more precisely the decay channels of the n = 3 and n = 4 resonances [44]. The n = 3 and n = 4 resonances [44]. The n = 3 resonance shows a preference for decaying into the n = 2 state of neutral H, which was expected

4 .O

3.0

- f 2.0 0

1 .o

because the spatial overlap is the best between a resonance and the next lower continuum. Detailed calculations confirm this tendency as higher thresholds are concerned 1391.

In addition to the fundamental character of H-’s being a real three-body system, photodetachment of H - encounters another peculiarity due to the degeneracy of the hydrogenic levels (in the non-relativistic approximation). Every n > 1 detachment threshold is the coalescence of all the nl thresh- olds. In other words, in the vicinity of an excited threshold, hydrogen has one more degree of freedom to adapt itself for trapping an extra electron. A permanent dipole can develop, the long-range interaction of which can have an important role on the dynamics of the outgoing electron [45].

In this respect, a comparison of the detachment reso- nances of H- with those of Li- can be very interesting, for Li excited states have the same quantum numbers as H, but they do not exhibit the same degeneracy. As will be shown below, no experimental data are yet available for lithium near the n > 2 detachment thresholds, but calculations show that except for fine details, the detachment cross-sections of Li- and H - are very similar [46]. This is attributed to the fact that only s-wave quantum defects are actually large in lithium, which shows how interesting it could be to extend similar studies to heavier alkalis. 3.2.3. Alkali negative ions. Alkali metal have actually attracted many theoretical studies of negative ions [3]. Alkali negative ions have the peculiarity that their second detachment threshold, which corresponds to the first np excited state of the atom, produces electrons of zero angular momentum (s-wave). In such a state, the radial potential does not form a centrifugal barrier, hence no shape reso- nance is expected, but as illustrated in Fig. 8 from Moccia and Spizzo [47], the opening of the ES detachment channel is accompanied by a pronounced “Wigner cusp” in the first EP channel [48]. This can be interpreted as a “virtual state’: [49], which is characterized by the fact that the scattering phase of the electron does not quite reach (n + f)n, whereas it would pass through (n + f)n if the energy passed through the levels of real resonances [49]. For heavier alkalis, the Wigner cusp is accompanied by more complicated reso- nance features [3, 501, that certainly deserve further experi- mental studies. Real Feshbach resonances can also be expected in lithium itself, in the vicinity of higher thresholds, for the neutral core is then more excited, hence more pol- arizable. The detachment resonances of the heavier alkalis

[45], @ 1992 The American Physical Society

Physica Scripta T58

i t I I

0 1 z 3 4 Photon energy l e v ,

Fig. 8. Photodetachment cross-section of Li-. The Wigner cusp in the 2s channel can be seen at the opening of the 2p channel. Reprinted with per- mission from [47] @ 1990 IOP Publishing Ltd and the authors.

Recent Experimental Achievements with Negative Ions 37

L.132 eV

I

c 2 2 2p2 + si 3s2 3p7 I / \U//,/,//////,/'

-0.033 eV \ -0.029 eV

-0.523 eV

2Pr-

ZD'L,

detachment ~ L U U U L L threshold

4 r s3A - 1

-1.263 eV -1.385 eV

Fig. 9. Similarity of the spectra of C- and Si-. A marked window reso- nance is expected below the threshold that opens the way to detaching an s electron [54].

take the form of pronounced minima below the upper detachment thresholds, that are named "window" reso- nances. Such a window resonance below the 6p (second) threshold was recently used to enhance excess-photon detachment of Cs- [5l] (see Chapter 5).

3.2.4. C - , Si- , Ge-. The ions C - and Si- are famous examples of negative ions with excited terms of the ground state configuration that still lie below the detachment threshold (Fig. 9). The negative ions C - , Si- and Ge- have received much attention in recent years especially for the window resonance, analogous to the one of heavy alkalis, that lies below the nsnp3 ' S 2 threshold [52, 531. This reso- nance was recently observed in Si- [54]. The excited bound level of C - was also used for the initial state in a photo- detachment experiment [55].

4. Negative ions in external fields 4.1. Negative ions in a magneticfield

A magnetic field has dramatic effects on the structure of continuum final states in a detachment experiment. The motion of the outgoing electron becomes quantized in the plane orthogonal to the magnetic field, and the detachment threshold is replaced by a series of Landau thresholds equally spaced by the cyclotron frequency. This induced structure of the detachment continuum was observed as soon as 1978 [56]. More recent calculations show that Feshbach resonances are also expected below every n > 1 Landau threshold [57] (Fig. lo), but no experiment has yet achieved a resolution high enough to make these very narrow resonances visible. Meanwhile, a high- resolution laser photodetachment study was carried out on 0- at energies well above threshold, which showed that the Landau resonances can still be observed in the continuum for a Landau quantum number greater than three thousand ~581.

4.2. Negative ions in an electric field In the presence of an electric field, the electron detached from a negative ion can escape either directly downward in

z 0 F 0 v)

fn fn 0 a 0

0 - 2 0 0 0 200 400 600

RELATIVE FREClUENCY (kHz)

Fig. 10. Threshold of the second Landau channel for photodetachment from a p-state in a magnetic field of 1.07T. The Feshbach resonance is so narrow that it hardly has any detectable contribution in the low resolution photodetachment around 45 GHz. Reprinted with permission from [57], @ 1992 The American Physical Society.

the exterior potential, or first go upward, and then be reflec- ted by the external field [59]. The corresponding inter- ference results in an oscillation of the photodetachment cross-section, which is very similar to the oscillation of pho- toionisation cross-sections of neutral atoms in the presence of an electric field [60].

The oscillation of a photodetachment cross-section as a function of energy in the presence of an electric field was first observed on H- [61], and later studied on the ions C1- and S -, which, in contradistinction to hydrogen, detach into an s-wave (Fig. 11). A quantitative analysis of the electric field induced modulation shows that its amplitude appears consistently reduced with respect to its calculated value C621.

The influence of an electric field on resonances is more difficult to predict. It can give appreciable information however on their internal symmetries. For instance the ' f l shape resonance of H- just above the n = 2 threshold has been found very stable in the presence of fields up to 24 MV m- [63], while the Feshbach resonances appear clearly split by the electric field [64]. Indeed a wealth of recently observed effects [65] remain to be studied in more

r'

3 0 0 cn zn 0

2 U

b

0 c

4

2

0

16260 16270 16280 16290 16300 Energy (cm-*)

Fig. 11. Modulation of the photodetachment cross-section of S- by an electric field of 97.5 kV/m. Quantitative discrepancies with calculations remain to be explained. Reprinted with permission from [62], @ 1993 The American Physical Society.

Physica Scripta T58

38 C. Blonde1

theoretical details : upper detachment thresholds can appear as shifted to lower energies, Feshbach resonances undergo field-assisted tunneling, new shape resonances can appear, that are induced by the field [65].

4.3. A.C.Jield and ponderomotive efects Free electrons cannot undergo transitions induced by a uniform plane-wave electromagnetic field, but the field has an important effect on their energy spectrum.

Because the electron has a forced oscillatory motion at the frequency w of the field, it acquires an additional kinetic energy, the average value of which is Up = q2E2/4m02 (with q the elementary charge, m the electron mass, E the ampli- tude of the electric field). In inhomogeneous electromagnetic fields, this extra energy has the role of a potential that can displace charged particles, e.g. in plasmas, hence its name of “ponderomotive potential”. The ponderomotive potential can be shown to actually act as a scattering potential for electrons emitted after multiphoton ionisation [66].

The effects of the ponderomotive potential can also be interpreted as modifications of the spectra of the atoms sub- mitted to a high intensity field [67]. Since the ponder- omotive potential actually is the minimum energy of free electron can have in the electromagnetic field, if the field frequency is low enough so that the deepest states of the atom are not much perturbed, the ionisation energy will be raised by Up.

The same should happen with negative ions, but the first measurement, of the photodetachment threshold of C1- in the presence of intense 1064nm radiation [68], seemed to indicate that the ponderomotive shifting of a detachment threshold could be significantly less than expected. Incom- plete shifting was also observed by photodetachment on the relativistic ion beam at Los Alamos: the two-photon detachment threshold of H - appeared raised by less than one half of the calculated ponderomotive energy [69]. But an electron-energy resolved measurement was performed, again on Cl-, which showed that time and space overlap of the ponderomotive-inducing and probing lasers has a criti- cal influence on the position of the apparent threshold [70]. The conclusion in this study and of an independent one [71] dealing with experimental two- and three-photon detachment of Au- is that detachment thresholds of nega- tive ions undergo ponderomotive shifting, in the same con- ditions as neutral atoms, by a quantity actually equal to Up within present experimental uncertainties.

The expression Up = q2E2/4mw2 shows that the lower the frequency, the larger the ponderomotive potential. Of course, the threshold shift cannot continue to increase indef- initely, but microwave fields, at GHz frequencies, could be expected to produce huge thresholds shifts. As a matter of fact, the kinetic energy spectrum of electrons produced from photoionisation of sodium Rydberg states by a 8.2 GHz field exhibits shifts of the order of Up, i.e. one eV for only a few kWcm-’ [72].

Photodetachment of a negative ion does not show exactly the same behaviour. Detachment with UV light of C1- ions submitted to a 2.6 GHz field did not reveal any threshold shift [73]. Solving the Schrodinger equation numerically in a simple model shows (Fig. 12) what the transition regime can be [74]. Threshold shifting appears when the intense field has a frequency high enough to bring the electron back

Physica Scripta T58

0.12 , , , , , , , , , , , , , ,

2. E .- 0.10 1

: 0.08:

n n

a C c

E 0.06’

0 c

g 0.02 a

0.00 . . . . 0.950 1.0100 1.d50 1.100

Photodetaching Field Angular Frequency

Fig. 12. Transition from the no-shift to the full ponderomotive shift regime in microwaves of different frequencies. The amplitude has been adjusted as a function of the frequency so as to always give the same value of the ponderomotive potential U,. Destructive interference makes the threshold shift to higher energies if the frequency is high enough to permit the ion to come back to the neutral core after half an oscillation in the electromag- netic field. Reprinted with permission from [74], @ 1989 The American Physical Society.

to the trapping core at each oscillation. Then destructive interference prevents the electron from going to a free state, unless it has been excited at least Up above the zero-field detachment threshold [74].

Subsequent photodetachment experiments of C1- and S- ions in the presence of a 2.7GHz microwave field yielded results that can be completely interpreted as photo- detachment in a static electric field, the amplitude of which would be equal to the instantaneous amplitude of the microwave [75]. It was even concluded that “under appro- priate conditions, the use of microwave fields is a good tech- nique for experiments on ions in static electric fields” [75].

This conclusion is especially striking if one remembers that neutral atoms seldom respond in microwave fields as in a static field and ponderomotive shifting of the ionisation threshold is not conditioned to the electron’s coming back after it took some distance from the atomic core. The differ- ence is that before ionisation is completed, the electron remains bound to the core even at far distances by the Coulomb potential. The microwave field is then very effi- cient at inducing transitions between the Stark-LoSurdo perturbed Rydberg series [76]. With this process in mind, one can easily understand that neutral atoms do not respond to microwaves as to static fields. The response of negative ions to a microwave perturbation at energies just below or above the detachment threshold is then one of the most important features of their specificity.

5. Negative ions in high-intensity electromagnetic fields 5.1. Introduction to multiphoton detachment

As neutral atoms, negative ions can undergo multiphoton excitation, in sufficiently intense fields. Since generally no other discrete level than the ground level is present below the detachment limit, the least energetic transition a nega- tive ion can make is multiphoton detachment.

Multiphoton detachment first provides a case of multiphoton-induced bound-free transition which cannot be perturbed by accidental resonances (either below or just

Recent Experimental Achievements with Negative Ions 39

above the detachment threshold). Multiphoton detachment thus embodies the perfect non-resonant bound-free multi- photon transition dreamt by all theorists. In addition, multi- photon detachment can be compared to multiphoton ionization to determine the influence of the Coulomb poten- tial on the outgoing electron. We had been looking forward to this comparison in the case of excess-photon absorption, as will be explained below.

Halogen negative ions are the most stable of all negative ions, because they have the same electronic structure as noble gases, which were used in most multiphoton ionis- ation experiments, but their detachment energies remain much smaller than the ionisation energies of the latter. Fruitful comparative experiments can thus be carried out with halogen negative ions, that do not require extraordi- nary laser illuminations. Three (for F-, Br-, I-) or four (for Cl-) photons of the Nd :YAG laser (1. = 1064nm) are enough to reach the detachment threshold, and the experi- ments appear quite feasible with commercial pulsed lasers.

When compared to single-photon detachment or col- lisional studies, multiphoton detachment still has the advan- tage of reaching a wider variety of final states, still with selectivity and coherently. Multiphoton detachment thus gives access to the phase relations between the different angular momentum channels of the continuum, which con- stitutes a quantitative test of the free-electron or plane-wave approximation for negative ions.

During the past few years, multiphoton detachment was the subject of repeated review articles [77, 781. The first multiphoton detachment experiments just aimed at measur- ing the generalized cross-section of the process. Despite many experimental efforts by several groups, the total cross- section measurements could never achieve a precision high enough to make a clear distinction between existing theo- ries. This situation pushed the experimentalists to look for other, more precisely measurable experimental parameters [79]. Such parameters can be reached only through photo- electron detection, which opens the way either to electron energy spectra or to photoelectron angular distribution measurements.

Total multiphoton detachment cross-sections should still be measured however, in order to make their behaviour clearer, as a function of the wavelength.

Of course, the larger the wavelength, the larger the number of photons required to reach the detachment threshold, and normally the intensity needed to saturate the photodetachment process should increase correspondingly, as is actually observed in the case of multiphoton ionisation.

Calculations by Crance [SO] have however indicated that multiphoton detachment saturation intensities could para- doxically decrease when the number of photons required to detach the ion increases. Davidson et al. [Sl] claimed that they have observed such an effect in multiphoton ionisation of Cl-, when comparing multiphoton detachment yield curves obtained at the two wavelengths 1064 and 190Snm. Interpretation of the multiphoton detachment signal as a function of intensity is hindered, however, by intricate effects due to the inhomogeneity of the laser beam, and the finite rise time of the laser pulse.

Because of the Wigner law, ponderomotive shifting of the threshold also dramatically changes the cross-sections. For all these reasons, complete spatio-temporal modelling of all

the processes that take place in the focus of the pulsed laser beam is required before one can conclude about the cross- sections. Just observing saturation as the bend of the detachment yield curve is not enough to give quantitative conclusions. For instance short infrared pulses are quite able to give a detachment signal that exhibits a sawtooth behaviour as a function of intensity, when successive channel closures occur well before the detachment process saturates [S2]. The first bend of the detachment curve should then not be necessarily interpreted as the signature of saturation.

5.2. Excess-photon absorption in negative ions It has been known for now fifteen years [S3] that multi- photon ionisation of a neutral atom does not necessarily produce electrons that have just absorbed the minimum number of photons required to reach the ionisation thresh- old. With sufficiently large laser intensities (and pulses short enough not to ionise all the atoms through the lowest-order process), the energy spectrum of photoelectrons shows a series of peaks equally spaced by the photon energy. Out- going electrons thus appear as having absorbed photons in excess, in a process which was originally named “above- threshold ionisation” or ATI. Numerous experiments in the eighties have studied the different regimes of AT1 [S4].

As clearly explained by Freeman [SS], our “efforts (. . .) to understand AT1 have been hindered by the infinite number of bound states near the ionisation threshold in a neutral atom, and the Coulomb coupling of the electron and the ionised atom, which allows the electron to exchange energy and momentum with the laser” while already escaping from the atomic shell. A negative ion appears in contradistinction as “the ideal system for observing excess-photon absorption (EPA)”. “The detached electron is essentially field free, which should remove any ambiguity about the origin of the higher-order EPA electrons”. Namely, if we can observe excess-photon detachment under the same experimental conditions as ATI, it is very likely that the faster electrons originate from a completely coherent process starting from the initial state.

The interpretation was confirmed by the observations, that showed excess-photon detachment occurring, first on the negative ion F- [S6] and, a few weeks later, on the ions C1- [87] and Au- [SS]. The experiment on F- was the only one however where the angular distributions (Fig. 13) of excess-photon detached electrons were measured. The

I

Fig. 13. Angular distribution of 4-photon detached electrons from F-, at the wavelength of 1064nm. At this wavelength, 3 photons are enough to detach the ion. The qualitative correspondence with the plane-wave approximation (dashed line) is the most precise signature of excess-photon detachment [86].

Physica Scripta T58

40 C. Blonde1

good qualitative correspondence of these angular distribu- tions with the calculated ones [86] is a complete signature of the coherence of excess-photon detachment in negative ions.

Strictly speaking, excess-photon absorption deserves its name only if the observed high-order processes have not momentarily become the lowest-order allowed processes because of channel closure by the ponderomotive threshold shift. A direct way to be sure that it is not the case is to perform an experiment with a pulse short enough to prevent the outgoing electron from recovering the ponderomotive energy during its ejection from the laser beam [89]. Only in this case are electrons with a kinetic energy higher than the photon energy unambiguous excess-photon electrons.

The experiment was performed with C1- ions submitted to lOOfs laser pulses [90], which clearly is a short-pulse regime. Fast electrons were observed that necessarily had high kinetic energies at the very time of their ejection, which gives definitive evidence that excess-photon detachment works as well without the assistance of channel closure. The resonances with instantaneously AC-shifted Rydberg states that can be seen in short pulse multiphoton ionisation experiments are here replaced by a smooth broadening of the electron energy peaks. Yet series of Wigner cusps have also been predicted, that should appear superposed to the classical series of kinetic energy peaks [91], but a higher kinetic energy resolution and a much better signal-to-noise ration seem necessary to make their observation possible.

Channel closure is not the only phenomenon that can enhance excess-photon absorption. A coincidence between first-order detachment with a window resonance in the con- tinuum can transfer a great part of the detachment prob- ability to the next excess-photon detachment channel. Such an experiment was successfully carried out with Cs- [Sl].

5.3. Multiphoton detachment diferential cross-sections Total cross-section measurements are not only imprecise, they also only put a mark on a one-dimensional scale. Multiphoton detachment angular distributions have the advantage of yielding a set of several parameters, i.e. a point in a multi-dimensional space, which is a more precise chal- lenge for theories.

Linearly polarized light sent onto a spherically symmetric target produces a distribution of photoelectrons of the form

with N the number of absorbed photons, P 2 k the Legendre polynomials of even order and 8 the angle between the pol- arisation and detection directions [92]. The asymmetry parameters f i 2 k contain all the atomic information that cal- culations are supposed to reproduce. In addition to the fact that the theoretical and experimental points now have to coincide in an N-dimensional space, the asymmetry param- eters can be measured in a much preciser way than total detachment cross-sections.

A set of two-photon angular distributions is presented in Fig. 14 [93]. One can clearly see that the plane-wave approximation always satisfactorily reproduces the qualit- ative shape of the angular distributions. F- appears as the ion which is best described by all theories, probably because it is the lightest, hence the smallest and the least relativistic

Physica Scripta T58

0,66 eV

270

0,84 eV

270

1,04 eV

21

kkl-usl 270

1,24 eV 90

0

270

1,30 eV Br-

270

1,60 eV

im 0

2m

Fig. 14. Angular distributions of two-photon detached electrons from halogen negative ions at the wayelength 532nm. The energy E (eV) is the kinetic energy of the outgoing electron. The large 2P,i2-2P,j2 fine structure of neutral I and Br makes it possible to experimentally distinguish two processes when photodetaching I - and Br-. The essential of the evolution of the angular distribution with E can be interpreted as a straightforward consequence of the Wigner law. The dashed line is the prediction of the plane-wave approximation [93].

ion of all the halogen. Nevertheless a very complete calcu- lation of two-photon detachment of F- [94], which takes electron correlations into account at every stage of the exci- tation, still lies more than two standard deviations from the measured angular distribution. The angular distributions that we have measured now are of such a precision that they will probably serve as an objective for successive improve- ments of the calculations.

Among general features concerning negative ions, it may be worth noting the nearly systematic relative minimum of electron emission that appears in the zero direction, i.e. direction of the exciting electric field, or polarisation direc- tion. This is a striking difference with the usual form of multiphoton ionisation angular distributions, which nearly all peak in the polarisation direction.

The difference between photoionisation and photo- detachment here is of purely quantal nature. The radial factors of the continuum eigenwaves in the Coulomb poten- tial have asymptotic phases that differ by 2n (at energies sufficiently low above threshold) for a pair of parity-allowed ionisation channels with AI = 2 [95]. Unless photoionisa- tion is perturbed by resonances or non-integer quantum defects, the natural behaviour of angular momentum waves

Recent Experimental Achievements with Negative Ions 41

is thus to interfere constructively in the electric field direc- tion.

Detachment final states of course are not the same. In the free electron approximation, they are free spherical waves. The corresponding radial wave-functions are asymptotically out of phase for successive angular momentum channels [96]. If only two channels are involved, as is always the case just above the detachment threshold, the interference is nec- essarily destructive in the polarisation direction.

The minimum of photoelectron angular distributions in the direction of the incident electric field is thus a quite general behaviour. It is not, but the way, a privilege of multiphoton detachment. The same minimum has been observed for years in single photon detachment as well, pro- vided that the detached electron does not come out of an s-shell. The angular distribution of single-photon detached electrons from 0- [97] is a beautiful example of this pro- perty.

5.4. Multiphoton detachment with elliptically polarized light Most photoelectron angular measurements are performed with linearly polarized light. Actually a more complicated polarization scheme would be of no use in the case of single- photon detachment, for single-photon angular distributions can always be analysed as the incoherent superposition of linear angular distributions, even if the linear components of the light have a well-defined phase relationship [98].

On the contrary, multiphoton excitation gives elliptically polarized light the opportunity to make its polarisation coherence active. Special formulae have then to be used to fit the corresponding angular distributions, and the number of atomic parameters given by an experiment can still be multiplied by a factor of two, with respect to linear angular distribution measurements [79].

Moreover, elliptically polarized light also has a remark- able property as a direct test of the plane-wave approx- imation. If multiphoton detachment perfectly enters the frame of the plane-wave approximation, then the angular distribution will remain insensitive to the orientation of the ellipse. In other words, a deviation of the angular distribu- tion from its four-fold symmetry with respect to the axes of the ellipse will reveal a departure from the plane-wave approximation.

This property made elliptically produced angular dis- tributions OUT clearest diagnostics about two-photon detached halogens. In the case of I - , a clear asymmetry became visible, while F- kept its symmetry unperturbed [99] . This confirms the conclusion of former studies, that F- is very satisfactorily described in the plane-wave approx- imation, while heavier ions require more sophisticated models. Care must be taken however to some special cases, e.g. C1- is expected to yield symmetrical angular distribu- tions at 532nm, but only due to accidental values of some phase-shifts which are in fact not zero [loo].

6. Conclusion

Recent experimental achievements with negative ions show a wide range of studies. Discrete states of negative ions exist! They appear as metastable states or detachment reso- nances. They provide the opportunity to study the discrete-

to-continuum coupling in an atomic spectrum without having to explore infinite forests of Rydberg lines.

The only atomic systems free from electron correlations may be hydrogen and hydrogenlike ions. In negative ions, electron correlations are essential to the stability of the dis- crete states. Negative ions are thus, with double Rydberg atoms [ lol l , at the forefront for experimenting new descrip- tions of collective motion.

The present status of experimental research with negative ions points the way to a few questions that will probably receive much attention in near future.

( i ) Are optical transitions such as the one observed in Be- exotic phenomena, or should we consider it as generally possible to study the emission spectra of negative ions? Many more excited resonances will certainly soon be observed in various ions. The search is difficult however, because resonance energies are seldom well known from theory, and a high resolution is required if one wants to see the sharpest Feshbach resonances that lie below the upper detachment thresholds.

(ii) Detachment in the presence of external fields is a very promising domain. Electrons photodetached in the presence of an electric field find themselves in a situation analogous to free-fall, the exact equivalent of which cannot be found in neutral atoms. In the presence of magnetic fields, a priority should be given to looking for the magnetic field-induced Feshbach resonances, the existence of which is predicted below the excited thresholds.

(iii) All mysteries of multiphoton detachment have not yet been completely fathomed. One important aim of the next experiments should be to check whether using a longer wavelength, hence more photons, really makes it easier to saturate the photodetachment process. A connection should be established between this oddness, if confirmed, and the special behaviour of negative ions in microwave fields.

Acknowledgements The author acknowledges with pleasure past and recent correspondence about their work on negative ions with T. Andersen, C. Pan, A. F. Starace and H. B. van Linden van den Heuvell. Thanks are due to M. Gustafsson and D. Hanstorp, who kindly let me read their unpublished comment about the electron affinity of oxygen. Especially valuable was the communi- cation by B. Christensen-Dalsgaard, H. Haugen and H. Stapelfeldt of their thorough numerical analysis of the multiphoton detachment experiment with Au-. This work was also supported by common work for several years on negative ions and many fruitful discussions with C. Delsart.

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