Chapter 4

Edward Gerjuoy is Professor of Physics (Emeritus) at the University of Pittsburgh. He is a theoretical physicist whose research has spanned a number of areas, including nuclear physics, plasma physics, and acoustics, but the bulk of his publications have been in atomic and molecular collision theory. He is a Fellow of the American Physical Society and in the past has chaired several Society Committees. Presently he is a member of the Society's Panel on Public Affairs and Vice Chair of its Forum on Physics and Society.

Early Theory. Atomic and Molecular Spectra

The foregoing understood, this overview begins with a discussion of the early (before about 1940) theoretical contributions to atomic physics that have been selected. Attainment of a more than rudimentary understanding of atomic physics necessarily had to await the advent of nonrelativistic quantum theory in its modern formulation, including the Schrödinger equation, the assignment of spin ½ to the electron, and the exclusion principle. Each of these crucial discoveries was published in European physics journals during the years 1925-1926. With very few exceptions, therefore, seminal atomic physics theory papers meriting inclusion in the CD-ROM did not appear in the pages of the PR before 1925. [One such exception is the contribution of Tolman (1924), showing that the value of the spontaneous transition probability from the upper level of a given spectral line, i.e., the Einstein A coefficient, could be inferred from line absorption measurements.] During the period 1925 through 1940, however, PR did publish a number of papers on atomic physics theory meriting inclusion in the CD-ROM or even in the book.

The 1926 European papers by Schrödinger showed that for purely Coulombic electron-proton interactions the Schrödinger equation yielded stationary state energy levels for atomic hydrogen that were identical with the energy levels obtained with Bohr's "old" quantum theory, the energy levels of which agreed very well with spectroscopic measurements. It also was known, however, that Bohr's theory had utterly failed to yield the energy levels of atomic helium, or of any other polyelectron atoms. After Schrödinger's triumph with atomic hydrogen, therefore, the obvious immediate task for atomic theorists was to determine whether the Schrödinger equation could correctly predict the measured spectroscopic properties of polyelectron atoms, especially their spectral line frequencies, relative line intensities, and selection rules. But the Schrödinger equation cannot be solved analytically for any atomic system with more than one electron, even when all non-Coulombic (e.g., spin-orbit) interactions are neglected and the mass of the nucleus is set equal to infinity (so that the atomic center of mass always resides on the nucleus). Thus after 1926 the actual immediate task for atomic theorists was to develop methods for approximating the bound state wave functions and energy levels that exactly solve the Schrödinger equation for polyelectron atoms; moreover, these methods had to be usable with the limited computational facilities available at the time.

Contributions to this task began to be published in PR only a very few years after 1926. Indeed by the late 1920s and early 1930s PR already had published a number of significant advances in the theory of atomic and molecular spectra. Slater's papers probably were the most influential of these contributions; in particular, Slater [Phys. Rev. 34 (1929)] introduced the still widely employed "Slater determinants," which automatically satisfy the requirements of the exclusion principle, including spin. Other important theoretical calculations of atomic energy levels and/or energy level spacings include those of Breit and Wills (1933) and Van Vleck (1934), who applied his so-called "vector model" approach to molecules as well as atoms. The paper of Mulliken (1933) is one of a series that also made important contributions to molecular energy level calculations. Breit and Rabi (1931) derived the so-called Breit-Rabi equation for the splitting of atomic energy levels in an external magnetic field, a result that Rabi used in his first attempts to develop improved methods for measuring nuclear magnetic moments (see the discussion of MBMR in the following section).

The molecular calculations described in the preceding paragraph were concerned primarily with the electronic components of the molecular energy when the nuclei of the atoms comprising the molecule lie in the vicinity of their normal equilibrium locations; other theoretical PR papers were concerned with the molecular rotational and vibrational energies, or with the shapes of interatomic potentials at internuclear separations far from equilibrium. In particular, Kronig and Rabi (1927) obtained analytic solutions to the Schrödinger equation for a rotating symmetric top (two equal principal moments of inertia), thereby yielding the exact rotational energies for a wide class of molecules; ammonia is an example. Morse (1929) introduced his famous "Morse potential" which, for a potential that very closely simulated actual internuclear interaction potentials, permitted exact analytic solutions of the Schrödinger equation for the nuclear vibrational energy levels of a diatomic molecule. Slater and Kirkwood (1931) considerably improved earlier calculations of the long-range van der Waals interactions between various pairs of atoms, e.g., two He atoms; their calculations later were further improved in the seminal Casimir and Polder paper (1948), which showed that taking the effects of retardation into account (which Slater and Kirkwood had not done) changes the long-range dependence of the van der Waals interaction from R^-6 to R^-7.

The most far-reaching early advance in our understanding of molecular spectra, however, undoubtedly was that of Condon (1926), who introduced the so-called "Franck-Condon principle." In this paper Condon, following up on a proposal by Franck (not published in PR) for explaining experimental observations of molecular dissociation by photons, postulated that electronic transitions (and consequent photon emissions) between two different interatomic potential curves of a molecule necessarily occurred too rapidly for any internuclear distances to change appreciably. On this simple postulate alone, Condon was able to deduce many of the previously very puzzling features of observed molecular band spectra.

Since about 1940 calculating atomic and molecular energy levels has increasingly become the province of theoretical chemists rather than theoretical physicists. Nevertheless PR has continued to publish important papers on the theory of atomic and molecular spectra. Indeed, during the 1940s Racah published a series of papers, one of which [Racah, Phys. Rev. 61 (1942)] greatly advanced Slater's formulation of the theory of atomic spectra. Also, in 1958 and 1959 Pekeris — using the Rayleigh-Ritz variational minimum principle and taking advantage of the vast improvements in computing power since the 1930s (though his computers were pitiful compared to today's, of course) — computed the energies of the ground and first excited states of atomic He to a heretofore unheard-of accuracy of about ten significant figures, including relativistic and other corrections; his calculations, wherein he diagonalized 1000 × 1000 matrices, illustrate the growing practice of expanding the sought-for solutions of the Schrödinger equation in function bases chosen less for their expected resemblance to the exact solutions than for their computational convenience.

Early Experiments. Magnetic Resonance

Early (once again defined as before about 1940) progress in experimental atomic physics did not have to await the advent of nonrelativistic quantum theory in its modern formulation. Thus a number of important atomic physics experiments were published in PR before 1925. Many of the seminal early experiments, however, though falling under the atomic physics rubric — e.g., the discovery of the Compton effect [Compton (1923)] or the discovery of deuterium [Urey, Brickwedde, and Murphy (1932)] — are discussed elsewhere in this collection. Therefore the remainder of this overview will concentrate on those significant atomic physics experiments, whether before or after about 1940, that other overviews are unlikely to more than barely mention.

One early and very clever experimental paper is on the Lawrence and Beams (1928) measurement of the time delay for emission of an electron in the photoelectric effect; Lawrence and Beams inferred that this time delay was less than 3 × 10^-9 s. Another experiment worth mentioning is that of Tate and Smith (1932), who passed electron beams through tubes containing gases (e.g., N₂, CO, and O₂) to measure the cross sections for ionization of the gases by electrons. Other than these the only early experimental papers published in PR that merit discussion are the marvelously ingenious and productive series of molecular beam measurements performed by Rabi and his co-workers, via what has become known as the "molecular beam magnetic resonance" (MBMR) method, which in this overview also denotes atomic beam measurements performed by basically the same magnetic resonance method.

Rabi's point of departure was the so-called Stern-Gerlach type of molecular beam apparatus exemplified in the work of Estermann, O. C. Simpson, and Stern (1937). In this type of apparatus, a molecular beam traverses an inhomogeneous magnetic field, and the molecular magnetic moment is inferred from the transverse displacement of the beam. Rabi's initial modification of the type of apparatus Estermann used was the introduction of a second inhomogeneous magnetic field, whose gradient was opposite to the gradient of the first inhomogeneous field traversed by the beam [see Kellogg, Rabi, and Zacharias (1936)]; by adjusting the gradients and traversal lengths, the transverse deflections of the beam in the two inhomogeneous regions could be made to cancel, whereby the molecular magnetic moment could be inferred without errors stemming from uncertainties in the beam velocity distribution (which had plagued the Estermann experiment). Rabi further realized that this cancellation, once established, would be destroyed if the molecules in the beam then could be induced to make transitions to selected new magnetic sublevels while traversing the beam path between the two inhomogeneous regions: the original cancellation had taken advantage of the fact that the moments of the magnetic sublevels had the same value in those two regions. Rabi's MBMR method of accomplishing such transitions to new magnetic sublevels was to introduce into the space between the two inhomogeneous magnetic fields an additional, homogeneous, magnetic field, which also contained a tunable oscillating field. The sensitivity of the aforementioned destruction of cancellation to the oscillation frequency then permitted extremely accurate measurements of the energy spacing between the selected sublevels.

MBMR was first described in Rabi, Zacharias, Millman, and Kusch (1938); with this MBMR technique Rabi and his co-workers were able to measure accurately not only the nuclear magnetic moments of the proton, deuteron, and other nuclei, e.g., Li⁶ and Li⁷, but also the quadrupole moment of the deuteron[see Kellogg, Rabi, Ramsey, and Zacharias, Phys. Rev. 55 (1939)]. Other representative important papers by the Rabi group [e.g., Rabi, Millman, Kusch, and Zacharias (1939) placed in the Science and Technology chapter] have been included in the CD-ROM. It is noteworthy that Rabi's ability to extract these nuclear moments from his experimental data rested strongly on his grasp of the early advances in molecular spectroscopy theory discussed in the first section; without a grasp of that theory, especially of how level splittings in magnetic fields are related to the various spin and orbital angular momentum quantum numbers characterizing the levels, Rabi would not have known how to interpret the (sharply resonant) oscillating magnetic field frequencies at which — for any given molecular species in his beam — there was marked destruction of the transverse deflection cancellation. In addition, to infer the deuteron quadrupole moment from his measured D₂ beam resonance frequencies, Rabi had to rely on calculated values (from the then best available D₂ molecular wave functions) of the electric field gradients that the molecular electrons produce at the deuterons.

Rabi-type MBMR experiments, with some improvements, continued to be published in The Physical Review after 1940. Ramsey (1949) pointed out that the sharpness of the MBMR resonances, and thus the accuracy of the MBMR experiments, could be increased significantly by having the molecular beam traverse two distinct oscillating field regions (rather than merely one such region, as in the conventional Rabi MBMR apparatus). With this sort of refinement, the distinctions between magnetic resonance measurements on molecules in beams and on molecules in bulk matter [as in "nuclear magnetic resonance" (NMR), which has revolutionized the imaging of biological tissues in vivo], began to blur. NMR, stemming from Purcell, Torrey, and Pound (1946) and Bloch, Hansen, and Packard (1946), is outside the scope of this overview. Ramsey (1952) presented a quitesophisticated theoretical treatment of the so-called "chemical shifts" seen innuclear magnetic resonance frequencies, a phenomenon of importance in both MBMRand NMR; as Ramsey discusses, these chemical shifts result from (in effect) magnetic shielding, by its surrounding moving and spinning electrons, of the magnetically resonating particle being studied.

Collisions. Experiment and Theory

A great many collision cross sections and other reaction coefficients are required for the full understanding of, for instance, fusion plasmas or the Earth's upper atmosphere. Starting well before 1925, therefore, and continuing to this day, atomic physics experimentalists the world over have been measuring such cross sections and reaction coefficients, for application as just indicated, and for the illumination such measurements can cast on the physical phenomena occurring in those collisions. The variety of "atomic" collisions that have been examined is almost limitless, including (and I am by no means being exhaustive) elastic scattering, excitation, de-excitation, and ionization of many species of atoms and molecules (in ground or excited states) by incident electrons, positrons, mesons, photons, neutral atoms, and ions (singly or multiply charged); electron capture by singly or multiply charged positive ions incident on atoms and molecules; dissociative recombination of molecular ions with electrons; etc. Of the many such experimental papers that have been published in PR, only comparatively few have been deemed sufficiently seminal to warrant inclusion in the CD-ROM.

An instructive 1959 experiment by Phelps illustrates the vast amount of information about collision rates that can be extracted, using modern techniques, from measurements on a gas (in this case Ne) in a container. Analysis of the measured optical absorption coefficients of various Ne lines enabled Phelps to infer, for a number of Ne excited states, diffusion coefficients, cross sections for collisional de-excitation by other Ne atoms, cross sections for collisional de-excitation by thermal electrons, and three-bodycollision rates. Dehmelt (1958) also used optical absorption measurements to infer the spin exchange cross section for collisions between thermal electrons and spin-oriented sodium atoms; the same experiment furnished an early direct measurement of the free-electron gyromagnetic ratio, determinations of which are further discussed in the next section. Knowledge of electron spin exchange collision cross sections in gases, notably NO, was the basis for the first reported evidence of positronium formation [Deutsch (1951)]. Madden and Codling (1963), using a chamber containing He, observed unusual (at the time) resonances in the He vacuum ultraviolet absorption spectrum that, in accordance with the theory of Fano (1961), represented photoionization of He(1s²) to various doubly excited, nominally discrete autoionizing levels [e.g., He(2s2p)] embedded in the He continuum energy spectrum; this experiment apparently was the first use of synchrotron radiation to obtain results of interest in atomic physics.

Modern techniques also have made it possible to supplement collision experiments of the sort just described, involving gases in containers, with experiments employing crossed beams of the colliding particles (which may include photons). One of the first examples of a modern crossed-beam atomic collision experiment is the Fite and Brackmann (1958) measurement of the cross section for ionization of H(1s) by electrons. Gallagher and Cooke (1979) used laser pulses to excite a beam of Na atoms to high-lying, singly excited Rydberg states below the continuum, e.g., Na(1s²2s²2p⁶18p), which levels then were ionized using a suitably delayed voltage pulse; these procedures enabled Gallagher and Cooke to determine the lifetimes of individual singly excited Na Rydberg states, the lifetimes of which were shown to be greatly reduced from their normally computed (zero temperature) values as a result of stimulated emission and absorption by the room-temperature blackbody radiation.

Predictions of collision cross sections of all sorts have been and still are the objectives of a large fraction of active atomic physics theorists. Comparisons of such predictions with experiment are used to test the theory and to reveal hitherto ignored physical effects (such as the above-described reduction of Na Rydberg state lifetimes by blackbody radiation). Reliable theoretical estimates of reaction rates also are needed because many collision rates important for the understanding of, e.g., plasma or atmospheric physics, cannot be measured in the laboratory. Since they generally involve solutions of the Schrödinger equation at energies in the continuum, however, calculations of collision rates of interest in atomic physics generally are much more difficult than the bound-state calculations discussed in the first section; for instance, calculations in the continuum cannot take advantage of the Rayleigh-Ritz minimum principle that has proved so useful for bound-state calculations (recall the Pekeris papers discussed above). Indeed, the difficulties with the continuum are so great that even today collision-rate calculations, though typically formulated to be consistent with the requirements of the exclusion principle, often assume the interactions are the dominant Coulombic-type only (in other words, often wholly ignore, e.g., the spin-orbit interactions that Slater's early bound-state calculations already were able to take into account).

For these reasons, significant publications in atomic physics collision theory did not appear in PR until after World War II. Many of these publications contain results of general interest to collision theorists in many fields, not merely to atomic collision theorists. The most obvious illustration of such a paper is the derivation [Lippmann and Schwinger (1950)] of the famous Lippmann-Schwinger equation, which reformulates the Schrödinger equation as an integral equation; unfortunately, use of the equation does not wholly avoid boundary condition problems in collisions involving more than two particles [i.e., in collisions even as simple as electron-H(1s) scattering], as Foldy and Tobocman (1957) showed. Another very important paper of general interest for collision theory is that of Kohn (1948), who derived a variational principle that is usable for computing collision amplitudes; although this variational principle is not a minimum principle like the Rayleigh-Ritz, and therefore has no built-in mechanism for deciding when a new approximation is an improvement over a previous approximation (as is possible in bound-state calculations), nevertheless the Kohn variational principle has been very widely employed in atomic collision calculations, often quite successfully. Furthermore, minimal (or maximal) principles do exist for some collision problems, as Rosenberg, Spruch, and O'Malley (1960) showed.

On the other hand, many atomic physics collision theory papers, like the 1961 Fano paper mentioned above, deserve notice in this overview even though they do not have as much general interest for collision theory as the papers discussed in the preceding paragraph. O'Malley, Rosenberg, and Spruch (1962) showed that the well-known "effective range" expansion for the low-energy elastic scattering amplitude, much employed in the analysis of nuclear collisions (which typically involve short-range forces plus a purely Coulombic r^-1 long-range repulsion between the colliding nuclei), must be modified for atomic collisions (wherein the dominant interactions between the colliding bodies, though Coulombic in origin and still long range, typically decrease more rapidly than r^-1, e.g., as r^-4). Gerjuoy and Baranger (1957) suggested that Breit-Wigner-type resonances [see Breit and Wigner (1936)], which have proved so useful for the unraveling of nuclear collision cross sections, should also be observable in atomic collisions; experiments, notably the crossed-beam experiment by Schulz (1963), have supported this suggestion. In 1953 Wannier, on the basis of a plausible, purely classical analysis (no quantum mechanics), predicted that near the ionization threshold the cross section for ionization of a neutral atom by incident electrons should be proportional to E^k, where E is the energy above threshold and

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The Lamb Shift. Tests of Quantum Electrodynamics

Although Pasternack (1938) already had suggested (from analysis of hydrogen Balmer line observations) that the 2²S_½ level of atomic hydrogen lies above the 2²P_½ level, the actual unequivocal demonstration of this fact by Lamb and Retherford (1947) made their paper one of the most important atomic physics experiments ever published. Unfortunately, because of space limitations, only the abstract of the definitive article (1950) could be in the book; the full text of this remarkable paper is on the CD-ROM. Theorists very soon recognized that the source of this deviation from the predictions of the Dirac equation was the interaction of the hydrogenic electron with the radiation field [see Bethe (1947)]; very soon thereafter, theorists were able to compute the Lamb shift using quantum electrodynamics (QED) in essentially its present formulation.

QED as such is beyond the scope of this overview; this overview does survey a few atomic physics experiments, however, that (like the Lamb-Retherford experiment) test QED predictions. In particular, great efforts have been expended on attempts to measure with high precision the deviation of the electron's gyromagnetic ratio g from the exact value 2 implied by the Dirac equation; the existence of such a deviation was first postulated by Breit (1947), though not from QED considerations. To lowest order in the fine structure constant , QED predicts the "anomaly"

Other experiments that should be mentioned include Rich and Crane (1966), who, trapping positrons via the techniques of Schupp, Pidd, and Crane, showed that to the accuracy of their experiment a_e for the positron equals a_e for the electron, a result required by charge, parity, time (CPT) reversal invariance; and Hänsch et al. (1975), who — with the aid of so-called "Doppler-free two-photon spectroscopy" — measured the Lamb shift of the hydrogen 1 2S½ ground state, i.e., the deviation of the hydrogen ground-state energy from the ground-state energy predicted by the Dirac equation (Lamb and Retherford had furnished information about the excited state 2²S_½ - 2²P_½ splitting only).

Masers and Lasers. Coherence

The invention of the maser [Gordon, Zeiger, and Townes (1954) and (1955)] rested on an understanding of the theory discussed in the first section for the energy levels of NH₃ (the molecule employed by Gordon, Zeiger, and Townes). In its ground-state electronic configuration — the only configuration of present concern — NH₃ has a complex line spectrum at microwave frequencies, resulting from splitting of the ground-state electronic energy by a variety of interactions, including most importantly the quadrupole coupling between the nitrogen nucleus and the molecular electrons. Gordon, Zeiger, and Townes were able to prepare a beam of NH₃ molecules in the ground-state electronic configuration that had inverted populations (more molecules in higher energy levels than in lower). When the beam was sent through a tunable oscillating microwave cavity, the power level in the cavity increased sharply (i.e., was amplified) when the cavity was tuned to an NH₃ spectral line frequency, because a net emission was being resonantly induced from those inverted populations. Gordon, Zeiger, and Townes invented the word "maser," an acronym for "microwave amplification by stimulated emission of radiation," to denote this amplifying operation of their apparatus. When the beam current was sufficiently high, however, the spontaneous microwave emission from the molecules entering the cavity was large enough to compensate for the microwave energy losses from the cavity, and the apparatus functioned as a very narrow band microwave oscillator, not merely as an amplifier.

These maser properties greatly increased the practicality of a number of important experiments. The hydrogen maser [Kleppner et al. (1965)], which employs a hydrogen atomic beam sent into a tunable cavity centered at the hyperfine splitting frequency of H(1s), has especially desirable properties and has enabled highly accurate measurements of that frequency {1420405751.800 ± 0.028 Hz according to Crampton, Kleppner, and Ramsey [Phys. Rev. Lett. 11, 338 (1963)]} and of its Stark shift. A hydrogen maser launched in a spacecraft has been used to verify general relativity-predicted frequency shifts [Vessot et al. (1980)].

Only three years after the invention of the maser, Schawlow and Townes (1958) published a design for an "optical maser" (not yet called the "laser"), which they believed would be able to maintain sustained oscillations at visible frequencies by taking advantage of externally induced inverted population levels in a "cavity" formed by a narrow tube with highly reflecting ends. The first to report an operating gas laser were Javan, Bennett, and Herriott (1961), who employed a mixture of He and Ne in a gaseous discharge. So much has been written about lasers, in the popular as well as scientific literature, that it appears pointless to devote any of this overview's limited space to further words about the laser's underlying physics, or to a summary of the myriad laser applications in science and technology. Semiclassical and more fully quantized theories of the laser have been given by Lamb (1964) and by Scully and Lamb (1967), respectively. An interesting scientific application of laser technology is that of Williams et al. (1976), who used lunar laser ranging to perform another test of general relativity. A number of "laser spectroscopy" schemes have been proposed for reducing the linewidths that complicate conventional spectroscopic observations. These schemes include Doppler-free two-photon spectroscopy, mentioned in an earlier section; "laser saturation spectroscopy," used by Hänsch et al. (1974) to obtain a precision value for the Rydberg (namely 109737.3143 ± 0.0010 cm^-1 ); and so-called "laser cooling" [Neuhauser et al. (1978)] to greatly reduce the velocities of the radiating atoms or molecules under study. Laser "trapping" of atoms and molecules was first envisioned by Ashkin (1970), who was able to laser trap micron-sized particles via radiation pressure alone.

Masers and lasers manifest their marvelous properties because they manage to induce many seemingly uncoupled atoms or molecules to radiate in concert i.e., "coherently"; correspondingly, these devices generate coherent states of the radiation field. Dicke (1954) gave one of the first instructive discussions of coherent radiation. The credit for the first thorough development of the quantum theory of optical coherence is owed to Glauber [Phys. Rev. 130 (1963)], however [see also Glauber, Phys. Rev. 131 (1963)]. Coherent states of the radiation field are related to so-called "squeezed states," wherein the fluctuation noise associated with one component of the radiation field is reduced at the expense of an increase in the fluctuation noise of a conjugate component [see Yuen (1976)]. Lasers have made it possible to observe other somewhat unintuitive consequences of radiation field coherence, including so-called "quantum beats," wherein photons of different frequencies appear to be interfering in a manner akin to acoustic beats. It is worth noting, however, that such quantum beats, between light waves originating from seemingly independent sources, were first demonstrated by Forrester, Gudmundsen, and P. O. Johnson (1955) before the invention of the laser, following a suggestion by Forrester, Parkins, and Gerjuoy (1947). In the Forrester apparatus, the light from a discharge wherein the Zeeman components had been separated by a magnetic field illuminated a photoelectric surface; the photoelectric current was passed through a microwave cavity, which manifested a sharp increase in output signal when (via variation of the magnetic field) the Zeeman splitting frequency was varied through the cavity resonant frequency. The Forrester experiment also was able to infer that the photoelectron-emission time delay was less than 10^-10 s, an improvement on the Lawrence and Beams result discussed previously.

Conclusion. Recent Trends

The atomic physics papers that have been discussed in this overview date predominantly from before 1970, for a number of reasons: Atomic physics is a long-established field; in any field of physics it is difficult to feel confident about the lasting merit of a paper that has been published too recently; and, the criteria for inclusion of a PR paper here rule out any that were published after 1983. Consequently, this overview, while hopefully meeting its objective of conveying a sense of the wide scope and great significance of the atomic physics papers that have been published in The PR, does not cover recent trends in atomic physics research. I will conclude, therefore, with a brief (certainly not comprehensive) survey of some recent atomic physics trends, especially those that seem likely to continue: (i) No let up in the bread-and-butter business of measuring and theoretically predicting collision cross sections and reaction coefficients of all sorts; the colliding particles are becoming more complicated, however (e.g., the collisions increasingly are involving heavier multiatom molecules), and chemists, both experimentalists and theorists, are increasingly performing such research. (ii) Increasing interest, theoretical and experimental, in the interactions of intense laser beams with atoms and molecules; the highly nonlinear couplings of the intense laser electromagnetic fields are difficult to treat theoretically and produce unexpected experimental results. (iii) Attempts to observe manifestations of chaos in quantum systems. (iv) Increasing interest in reactions of all kinds involving atoms in highly excited Rydberg states; such reactions test approximations (e.g., certain classical treatments), which are rarely examined in collisions involving atoms in lower states and also are thought to provide a vehicle for investigating quantum chaos. (v) Employment of polarized particles (atoms, electrons, etc.) in experimental investigations of collision rates; such experiments can yield otherwise unobtainable results and put greater strains on the theory. (vi) Use of high-energy particle accelerators to perform atomic physics experiments; by using merged-beam techniques, such experiments can even yield collision cross sections at very low energies in the center-of-mass system. (vii) Ever more accurate measurements of fundamental quantities, including some not mentioned in this overview (e.g., of the Lamb shift in He⁺), taking advantage of laser cooling, single-atom trapping, etc.; such experiments should provide new tests not only of QED, but also of proposed theories violating parity conservation and time-reversal invariance. (viii) And finally, more frequent undertakings by atomic physics theorists of arduous "a priori" numerical computations that rely on the largest and fastest available computers and have little or no recourse to physically insightful approximations.