REVIEW OF ELECTRIC AND MAGNETIC CONFIGURATION-MIXING EFFECTS IN ATOMIC SPECTRA

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REVIEW OF ELECTRIC AND MAGNETIC

CONFIGURATION-MIXING EFFECTS IN ATOMIC SPECTRA

W. Garton

To cite this version:

W. Garton. REVIEW OF ELECTRIC AND MAGNETIC CONFIGURATION-MIXING EF- FECTS IN ATOMIC SPECTRA. Journal de Physique Colloques, 1982, 43 (C2), pp.C2-1-C2-12.

�10.1051/jphyscol:1982201�. �jpa-00221810�

JOURNAL DE BHYSIQUE

Colloque C2, supplément au n°ll, Tome 43, novembre 1982 page C2-1

REVIEW OF ELECTRIC AND MAGNETIC CONFIGURATION-MIXING EFFECTS IN ATOMIC SPECTRA

W . R . S . G a r t o n

Blackett Laboratory, Impérial Collège of Science and Technology, London SW7 2BZ, U.K.

Résumé

Les résultats surprenants des études expérimentales et théoriques récentes concernant l'effet de champs électriques et magnétiques sur les spectres atomiques sont examinés. Nous nous intéresserons tout particulièrement aux structures qui existent dans le continuum de photoionisation .et aux.processus qui en sont .la cause.

Des exemples des conséquences du mélange de l'effet Paschen-Back et du diamagné- tisme (a) et de 1'autoionisation forcée (b) seront présentés.

Abstract

The surprising results of recent and current experimental and interpretive work on electric and magnetic field effects in atomic spectra are reviewed, with emphasis on processes responsible for spectral structures in regions of photo- ionization continua. Cases of (a) mixture of Partial Paschen-Back structure and Diamagnetic Shift, and (b) of "Forced autoionization" are presented.

What follows is an attempt at a short coordinated review of much fine recent work on Stark and Zeeman spectroscopy of long Rydberg series. Two well presented articles of review type which cover much detail have been written by Gay (1980) and by Feneuille and Jacquinot (1981).

The significance of Stark and Zeeman effects in the history of fundamental atomic and molecular physics, and in applications in chemical physics as well as to laboratory and astrophysical plasmas, is well known. In retrospect it is perhaps surprising that the Zeeman effect was discovered first (1896), and the Stark some 16 years later, because we might suppose that potentials of tens of kilovolts necessary for the latter would have been more easily achieved, at the

turn of the century, than large magnetic fields - bearing in mind the kind of spectroscopic resolution then available. Part of the time gap doubtless resulted from the problem of sustaining the necessary electric field across the low press- ure gas needed for observation of decently sharp spectral lines. Stark

essentially solved the problem by an early type of atomic-beam experiment, - the "Canal-ray" tube. As will be seen in this review the great surge of novel work, on both electric and magnetic effects, of the last 6 or 7 years has largely depended on the application of modern atomic-beam techniques, combined with introduction of tunable laser systems and their utilization in ingenious ways.

An illustration of the pace and novelty of the new work is as follows. Five years ago, CNRS Colloquium No.273, concerning mixing of atomic and molecular

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982201

C2- 2 JOURNAL DE PHYSIQUE

energy states, was held in Aussois. A few papers (cf. Jacquinot et al. 1977;

Kleppner 1977), concerned field effects in Rydberg series. For the present review the writer assembled, and at least digested in part, about 50 papers, nearly all post-1977, and equally divided between electric and magnetic effects.

Moreover, the great majority of papers carrying experimental results have been based on laser spectroscopy combined with either atomic beams or the technique of themionic ionization chambers. Many surprising results have emerged, and these have quickly produced new concepts for interpretation, and have stimulated basic theory. It is worth noting Rau (1979), who, in a discussion of the "near zero-energy resonances1' observed for atoms in electric and magnetic fields, remarks: "Each new feature that has emerged - (i.e. from experiment) - ^{has been}

viewed as surprising and not irmnediately accounted for".

A number of recent papers cite as the first of these observational surprises the photographic absorption spectra of Ba I in a magnetic field, obtained by Garton and Tomkins (1969). These early spectra w y e a great improve- ment in resolution on the pioneer effects of Jenkins and Segre (1939) who studied Na I, and showed a lot of complex detail of

and n-mixing, but the surprise lay in the presence of nearly equally spaced resonances in the zero-field photo- ionization continuum. These resonances, with a spacing near the zero-field limit of 1.5 times the cyclotron interval, attracted attempts at theoretical explanation, (e.g. Canuto and Kelly, 1972; O'Connell, 1974; Garstang 1977; Rau 1977), and Starace (1973) produced, from a

approach, a family of curves versus magnetic field B; these curves showed the transition of the spacing from 1.5 to

far from the ionization limit. The resonances have subsequently been referred to as "Quasi-Landau1', for obvious reasons (cf. Edmonds 1970).

It seems now trivial and accidental that the magnetic (QLR's) were the first of the surprises, because several other equally unanticipated experimental observations have followed, which have certainly had to await exploitation of the much more elaborate and sensitive systems of laser spectroscopy. This remark applies particularly to electric field effects.

As regards Zeeman structures around and beyond the ionization limit, great improvements of contrast and structure were achieved by use of a super- conducting solenoid, enabling separation of

and absorption spectra

(Lu et al. 1978a; Garton et al. 1980). Examples of the appearance of the Ba I, Sr I spectra versus field are shown in Fig.1. More accurate check of the calculations of Starace (1973) was possible from these spectra and from corresponding measurements with a scanning photomultiplier; (see Figs-2 and 3 ) .

FIGURE 2. q.L.r. separations for Ba I against energy, at B = 4.69 T, measured from zero-field limit; full curve represents

Starace plot,

1.6

2-

% I* ^,.,

I ~ I I I ~ I ~ I ~

,

I error

1 1

. 4

~

: ;

1 . 0 . ' 1 1 I I ' "

0 100 200 300

q.L.r. separation/om-'

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Famts

3.

dashed line is cross-section for B = 0.

In parallel with photographic work on well-resolved spectra, the first results of Zeeman structures within and beyond the zero-field ionization limit of long Rydberg series, by tunable laser techniques were reported in three papers.

(Fonck et al. 1977, 1978; Zimmerman et al. 1978). The first two papers reported positions and separations of the QLR1s for the case of two-photon transitions

(even-parity excited states) in Ba I and Sr I. The experiments were carried out at Argonne by use of a large superconducting dipole magnet provided by Rutherford SRC Laboratory, and capable of 4.6 Tesla. The results provided a much improved test of Starace's (1973) calculations, and confirmed also the theoretical expectation (Fano 1977, Lu et al. 1978a) that the QLR phenomenon would be seen for upper states having 1 - !mi of even parity. In the photographic spectra mentioned above, this correctly implied resonances in the (I--spectrum, whereas in the case of the experiments of Fonck et al. (1978), they appear in the

f l -spectrum. Fig.4 represents some of the results of Fonck et al. (1978).

The QLR1s are seen to extend considerably on both sides of the zero-field limit, and to correspond well with the WKB-type plots of Starace (1973). The work of Zimmerman et al. (1978) concerned measurements, at good resolution, of the structures of Zeeman manifolds in Na I, in the range n=25 to 31 of Rydberg even- parity states. They were thus studying the region essentially of 9.-mixing and the early onset of n-rnixing. The alkalis are generally accepted as having the attraction to the interpreter of possibly simpler behaviour than an alkaline earth. In the present instance, Zimmerman et al. (1978) were able to accommodate very well their measurements by diagonalising the energy-matrix for the Na I atom in the magnetic field.

The work of Economou et al. (1978) was also on an alkali atom, viz.

Rb I. Using laser spectroscopy and a themionic ionization chamber within a

superconducting solenoid, they were able to study both single and double photon

transitions, and were able to follow, as did Fonck et al. (loc.cit), resonances

well below the limit, and to confirm the Starace model. Up to this time, all

experiments, photographic and laser-type, had confirmed the interval near the

limit as being 1.5 times the cyclotron interval. The next surprise was reported

by Lu et al. (19788), from photographic absorption spectra of Li I, obtained

with the solenoid magnet. This time, the QLR phenomenon was observed, but with

Fig. 4 - Resonance positions as a function of a.

The two data points defined to agree with the theory are marked by the arrow. Circles. Srr resonance peak positions; crosses, Bal resonance minimum positions;

triangles, BaI peak positions. The lowest datum point corresponds to the

's, level.

an interval of half the cyclotron frequency. These workers simultanecusly noted the appearance of even-even (forbidden) lines. The results were quicklyexplained as due to the motional electric field produced by the thermal motion of this light atom in the magnetic field, (Crosswhite et al. 1979).

Fonck et al. (1980) give an amplified discussion of the work reported in their 1978 paper, and conclude that the

model calculations of positions and separations of the QLR'S represent the experimental findings better than the modified Bohr model of Canuto and Kelly (1972), Garstang (1977) or O'Connell

(1974). As regards the theoretical interpretation these models cited are semi- classical, semi-empirical, but are found useful practically. More mathematical approach (Fano 1977, 1980; cf. also Lu et al. 1978a), while giving a basis of improved insight, offers such complex sets of coupled equations as to inhibit computations at the present.

Until 1980 the Zeeman spectra in the region of n-mixing, obtained either as photographic absorption spectra or by tunable laser techniques, appeared so confused as to be uninterpretable. The position has now changed greatly, not by solution of the computational problems mentioned, but by highly skilled experimental technique and interpretation of the results. Papers by the Paris group (Gay 1980; Gay et al. 1980; Delande and Gay 1981), and by Castro et al.

(1980) at MIT, have between them yielded much greater insight. Both groups

exploit the high to very high resolution achievable with tunable lasers. As an

example, until these reports, F.S. Tomkins and the writer believed we had

observed the longest Rydberg series to date, viz. Ba I n ' P ? to n=105;

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this was achieved in the third order of the 9.4 Paschen circle at Argonne over 10 years ago. The Paris group, working with Cs, have been able to follow the n 2~ levels to n

162. Interalia this work has shown it possible to realise and handle in the laboratory Rydberg atoms in the energy range of important significance in radioastronomy.

In addition to providing much improved resolution, the experiments by laser spectroscopy have the great advantage over photographic work - even with the pretty good resolving power achievable with a large grating - that detailed change of structure in the spectrum can be followed as the magnetic field is changed in small steps. In ~hotographic work this is rather precluded by the time taken in acquisition of a limited number of exposures and a not inexhaustible supply of liquid helium for a superconducting magnet. The fine results of the Paris and MIT groups stem from these advantages. Moreover, both groups have improved on the results of Fonck et al. (1978), by basing the tracking of QLR structure below the zero-field limit on a well-resolved leading line of each manifold in the region of confused n-mixing. The MIT group concerned themselves with structures below the limit for Na I even-parity states, and the Paris group, who use very high resolution laser systems, have studied the odd-parity states of Cs I, from well below the limit to about 100 cm-l above; incidentally in Ba I, Garton and Tomkins (1980), were able to follow to about 300 cm-l.

Of course, the latter element - and Sr also - is attractive to the experimenter because the oscillator strengths of the very high series lines decline a good deal more slowly than in an alkali. On the other hand the attraction of the alkali elements is that it is possible to work on much more H-like states, with resulting simplification of interpretive theory and computation.

Although the foregoing will have conveyed that basic theory seems to have lagged on experiment in the field concerned, we have to note the careful calculations of positions and oscillator strength distributions in recent work of Clark and Taylor (1980) for the H-atom. This is a case where experimental checks will be very difficult, and we are likely to depend for some time on the theoretical results.

An interesting case of magnetic interaction has been observed by us in absorption spectra of In I: a portion of the spectrum is shown in Fig.5.

We here have a case where partial Paschen-Back splitting is present together with diamagnetic quadratic shift. As explained by van Vleck (1932), the former can be represented as a power-series in the field B, so apart from the linear splitting there is a quadratic term representative of the spin-anomaly of the electron, which has no connection withthequadratic effect associated with diamagnetism. van Vleck states, what is true for one-electron systems, that the two quadratic shifts are mutually exclusive. However, this is not true for In I, since spin-orbit splitting remains high at values of n (say about 20), where the diamagnetic shift becomes important at fields of tens of KG, (cf.

Neijzen and Donszelmann, 1981). As far as we know the quantum mechanical formulation of the problem of simultaneous presence of both shifts has not been given previously, We have handled this problem and we obtain results, to appear shortly, which agree well with the observations of positions and intensities of the components of the Zeeman patterns, for the range n=16-25.

Turning to electric-field effects, as much - probably more - ^modern

experimental work has been reported, and has been done almost entirely by means of laser-atomic-beam spectroscopy. Earlier notable work had, of course, laid the foundations of our understanding and given at least a primitive basis for interpretation of the several surprises which have emerged in the last 5 years.

The theoretical problem of the single-electron atom in an electric field has long been considered as more tractable than the corresponding magnetic case, because the wave equation in the former is separable in parabolic coordinates, i.e. suitable quantum numbers can be defined. In fact, it has been said that one of the greatest successes of early quantum theory - preceding by 10 years the formulations of quantum mechanics - was the solution of this problem by Epstein (1916) and by Schwarzschild (1916). In the limited space and time available the present review will concentrate most attention on field-

ionization processes without much detail on the excellent work reported recently

Figure 5 - and 6-structures in In I, 4.5 T, showing Partial Paschen-Back and Diamagnetic Shifts.

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on Stark manifold structures of lower energy states. However, in passing we should note the important studies in the latter regard of Littman et al. (19761, Zimmerman et al. (1979), on all the alkali atoms in much detail.

A problem of long standing concerns the process by which an atom (single- electron for simplicity) becomes ionized in an electric field. Regarded in simplest terms it is conceivable that a hydrogen atom in its ground state could be subjected to an electric field large enough to overcome the Coulomb force.

An easy calculation shows this will require a field of 5 x lo9 Vlcm, - ^not

practical in the laboratory. Obviously, the case is quite different for high n states. Fifty years ago and more a good deal of attention was given to the problem of field ionization, especially by astrophysicists concerned with modelling of stellar atmospheres. Calculations of this sort involve use of Saha's ionization equation which, it will be recalled, contains partition functions of two ionization stages, and the ionization energy in an exponent.

The long-standing problem was what value to use for the latter and where to terminate the art it ion functions, under the recognition that the microfields of ions and electrons present in a thermally ionized gas would "depress the ionization potential", and simultaneously destroy the higher bound energy levels. p good early example of treatment of this problem is found in a paper by ~nszld (1947), in relation to astrophysical application, and about 30 years ago the group of Lochte-Holtgreven in Kiel became much concerned with these questions, in the course of the celebrated programe of work with high-current arcs. bough at those dates the distinction between what, in recent papers, are referred to as "saddle-point" and "tunneling" processes was recognised, vastly more insight into their relationships and complexities have emerged from the several surprises met in recent experiments by laser spectroscopy.

In an important paper, Littman et al. (1978) report maps of Stark manifold structure versus electric field for Li I states in the region n 19, i.e.

fairly - though not very - high Rydberg states, Their results highlighted the complete conflict of the "tunnel" and "saddle-point" approaches, and made clearer the role of core penetration by the valence electron, that is to say the differendes of behaviour of the Stark structures for H-like states and those of many-electron atoms become clearer. In particular, it was concluded that, while the saddle-point model could not be invoked for H-like states -

neglecting relativistic removal of degeneracy - it would be relevant for all states of appreciable quantum defect, and would in fact have some formal resemblance to the configuration-mixing effect of autoionization.

At the previous Aussois meeting, Jacquinot et al. (1977) reported another surprise, in the discovery by high resolution laser experiments, of very sharp discrete structures well above the "saddle-point" in Rb I. This work is more fully described by Liberman and Pinard (1979). Again, the very high resolution obtained is illustrated by the fact that these workers were able to follow zero-field series to n - ^100. The sharp resonances referred to were seen in d -polarization not in fl , and consideration of the nature of the full potential-energy surface for an electron in combined Coulomb and external electric field along the z-axis - instead of taking account of just the cross- section by a plane x=O, y=O - gave qualitative understanding for the ekistence of these resonances. They are so sharply defined, i.e. so insensitive to external perturbation, that they are isotopically selective.

Another paper (Feneuille et al. 1979) follows up the work and ideas which emerged fromthe several recent papers above cited. In addition to the

extremely sharp C -resonances in Rb I, they found generally weaker resonances

in

These were, by ordinary spectroscopic standards, quite

narrow (0.005 cm-I), but the very high resolution of the equipment enabled the

resonance shapes to be examined. These proved to be of Beutler-Fano type,

providing a pretty confirmation of the autoionization analogy suggested by

Littman et al. (1978). Yet another complication and surprise, of the sort

referred to in the previous quotation from Rau (197?), was contained in the

paper by Freeman et al. (1978a), reporting discovery of electric-field induced

resonances in Rb I, in fl- ~olarization, not only above the saddle-point limit,

but above the zero-field ionization potential! While the structure between these limits had been interpreted as set out above, the explanation of these electric analogues of the QLR's of the magnetic case was not obvious. In the magnetic case it is easy to see that quasi-stable states can arise from periodic motion of the electron in the combined B and Coulomb fields, but this condition

is more difficult to visualize in the case of the electric field.

However, these new experimental surprises have been the subject of further observation, measurement and penetrating analyses by Freeman and Economou (1979), by Luc Kernig and Bachelier (1979) and by Rau (1979). Other work, under the heading "Continuum Stark Spectroscopy1', has been described by Luk et al. (1981), in this case in Na T. Again, well resolved structure was found between the saddle-~oint and zero-field limits with pronounced Beutler- Fano profiles, and marked oscillatory structure indicative of quasi-stable levels above the zero-field limit.

In addition to work on normally bound states and into the annexed continua, several experiments have been aimed at study of effects of electric fields on doubly-excited states, which exhibit large widths and/or ~rofiles characteristic of normal autoionization. Thus, Freeman and Bjorkland (1978b) studied the changing shape and structure of autoionization resonances in Sr I, having upper states of character (42~)nR with n

12, versus electric field.

The observations were interpreted by comparison with calculations of the H-like manifold of Stark sub-states. Cole et al. (1980a,b) undertook an ambitious

experiment with synchrotron light, well into the vacuum uv, in observing absorption spectra of inert gases (A, Kr, Xe) in and around the region between the inverted p5 2~3/2 limits, i.e. where some of the first autoionization resonances were disco+ered by Beutler in the 1930s. The experiments faced the problem cited above of maintaining the necessary high voltage across the low- pressure gas cell. This was solved by working at pressures well below the Paschen minimum of the electrical breakdown curve, and offsetting the decreased gas density by using a long path. One of the most interesting results was a demonstration of "forced autoionization" or - as Cooper et al. describe it

"electric field induced autoionization". This effect was probably first mentioned as explanation of some spectra obtained in Ba I at Harvard 20 years ago (Garton et al. 1962). Fig.6 shows a comparison of the absorption spectra of Ba I respectively obtained with a furnace and a shock-tube plasma. We observe that under the latter conditions ( T N 6000 degrees, p-several atmospheres), the high series lines 6 lSO* 6snp lpl disappear, and the levels 5d8p 3 ~ , 3 ~ , which are sharp under furnace conditions, become much wider in the shock tube spectrum. The explanation given at the time was "forced autoionization" due to the microfields in the heavily-ionized shock-tube plasma.

Admittedly, the interpretation was somewhat inferential, and the experiments of Cooper et al. (1oc.cit) provide the first clean demonstration of the process.

Specifically, the effect of the applied electric field is to embrace an extra

"Beutler-Fano" resonance corresponding to a state, which in the absence of the field, lies below the first ionization level and is sharp. Some impressive work just recently reported by Okasaka and Fukuda (1982), who have worked with electromagnetic (instead of aerodynamic) shock plasmas, seems to have produced a pretty case of a Beutler-Fano "window-type" resonance in Ca I, "forced" by the plasma microfields; the state concerned in this case is 3d5s 3 ~ . Incidentally, this work is a good illustration of a point emphasised at the earlier Aussois meeting (Garton 1977), that there might be good prospects of observation of new autoionizing transitions from emission sources, under the right circumstances,

Other work on electric field effects on autoionizing states has been reported by Safinya et al. (1980). This particular group of workers at Stanford had already announced elegant and novel detailed work on autoionized transitions to states based on the excited 2~ levels of the alkalike earth ions -

e.g. states like Ba I (6p 2~ nR, which lie far above the first ionization

potential. In the paper men?Loned they described interference effects from

measurements of the electric-field dependence of the positions and widths

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-

^In-

of states like (6p P)17s, 15d, 12R (1= 2 4 - lo),

The final experimental surprise to be noted here was found in the latest paper by the Paris group (Feneuille et al, 1982), reporting a further study of Rb I. From the earlier work at MIT (Littman et al, 1976), the sharp increase in ionization rate versus field in the neighbourhood of the saddle-point limits was recognised and understood in principle. What Feneuille et a1,(1982) have discovered, by high resolution and detailed analysis of the dependence of Stark states on field, is the reverse, - a localised decrease in ionization rate, i.e. a stabilization of a particular Stark level by the external field.

Again, this unexpected result is accompanied by a reasonable explanation, in this case in terms of the perturbation produced by spin-orbit interaction.

Because of the brief nature of this review, full justice cannot be done to the large range of novel and ingenious use of tunable laser spectroscopy, or to the penetratiw analyses and interpretations, though it is hoped the

above notes will serve to emphasise the very exciting nature of recent and current researches on field effects, In any event the major groups active in the fields of work concerned are represented in the present Proceedings, and their articles will provide necessary detail, It seems certain that the immediate future will see experiment extending further into the vacuum ultraviolet, both by surveys with as high resolution photographic instruments obtainable, and by exploiting

tunable laser spectroscopy in very high resolution systems, In this way we can expect further surprises from the wider range of atomic species which can then be studied. Preliminary efforts in this direction are already in hand in Bonn and in Maryland, in this case on magnetic effects studied photographically with large superconducting magnets of both types.

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Addendum at time of Meeting

Regarding the discussion and statements on "forced autoionization" on p. 9, the

author became aware of a serious omission. A demonstration of controlled occuren-

ce of this process had already been provided in the work of T.F. Gallagher and

co-workers

see this article in the present proceedings for details andreferen-

ces .