Atomic, Molecular and Optical (AMO) Physics is one of the most rapidly advancing of the physical sciences. Spurred by numerous recent and remarkable technological innovations, and by the growing recognition of its relevance to nearly all aspects of modern scientific endeavor (from tests of fundamental symmetries to biochemistry to medical imaging and to astronomy and cosmology), AMO physics now encompasses a bewildering panoply of phenomena, techniques, ideas and applications. The most recent national meeting of AMO physicists highlighted, for example, talks on quantum cryptography and quantum computation, the trapping of individual atoms and ions, atomic timekeeping, collective phenomena in ultracold gases and Bose-Einstein condensates, the slowing and stopping of light, non-linear optics, plasma processing, ultra-relativistic ion-atom collisions, and the coherent control of chemical reactions.

Underlying many (if not all) of these new developments is a fairly elementary understanding of what atoms are and how they work. The rules of quantum mechanics (the theory of AMO physics) were firmly established in the first half of the twentieth century and have not changed significantly since that time. The predictive power of the theory has changed dramatically, however, due to enormous improvements in computational technology and to the increased sophistication of theoretical techniques for treating complex and highly-correlated physical systems. The combination of elementary fundamental principles and improved predictive power lends some coherence to the disparate endeavors that comprise AMO science. While experimental advances continue to expand the boundaries of the field, it is the underlying theory that unites those efforts into an identifiable intellectual discipline.

There remain, however, outstanding fundamental questions that continue to inhibit progress in AMO theory, with the result that a wide variety of physical processes remain far beyond current theoretical and computational capabilities. The vast majority of these derive simply from the long-range nature of the Coulomb interactions between the electrons and nuclei that comprise atoms, molecules and ions.

For matter in its ``normal'' state, the morphological organization of electrons and nuclei minimizes these long-range interactions, observable only as residual dispersion (polarization or van der Waals) forces between electrically neutral fragments [PRA 50, 2841 (1994)]. Even in such relatively benign circumstances, long-range interactions largely dictate the dynamics and correlations attendent to dissociative or associative chemical processes and to collective phenomena in solids, liquids, gases and the novel supercooled phases of degenerate Fermi gases and Bose-Einstein condensates.

For highly excited or ionized matter, on the other hand, the long-range Coulomb forces between atomic fragments result in infinities of reactant and product states in small energy intervals. In the excitation of a target atom by electron-impact, for example, an infinity of excited (or Rydberg) final states of the target can be excited by any incident electron with kinetic energy greater than the first ionization potential of the atom. Such ``infinities'' are, of course, the source of both the richness of phenomena and the ultimate failure of theory's predictive power.

My efforts to contribute to the advance of AMO theory have focussed on a better understanding of both the nature and consequences of long-range interactions. First and foremost, I have endeavored to assist in-house experimental studies of Rydberg atom dynamics by modelling the redistribution of Rydberg state populations in collisions and/or in external electromagnetic fields. This ten year collaboration with the experimental group of Keith MacAdam has resulted in a better understanding of the redistribution of Rydberg states attendant to both inelastic collisions and charge-transfer processes. We identified, for example, large tunneling contributions to charge transfer superimposed upon a new quasi-classical ``three-swap'' mechanism for low-velocity ion-atom collisions [PRL 75, 1723 (1995)]. We subsequently predicted an unambiguous signature (as yet untested experimentally) of three-swap capture events that should provide a stringent test of classical models of the charge-transfer process [PRA 57, R13(1998)]. At the urging of Eric Hessels, we also used our familiarity with charge transfer processes to propose a scheme for the formation of antihydrogen atoms at the antiproton storage facility [PRA 57, 1668 (1998)].

The redistribution of Rydberg states due to distant collisions and to microwave radiation was successfully modelled and interpreted. For distant collisions, high-order dipole interactions were found to resonantly drive Rydberg atoms into high angular momentum states, quite analogous to multiphoton excitation processes [PRA 52, 2865 (1995)]. For microwave processes, a multiphoton excitation picture again proved applicable, but the periodicity of the microwave field had to be reconciled with the slow (or adiabatic) response of the charge cloud to the imposed field. This required the development of a new ``low-frequency'' Floquet theory based upon a discrete-time picture of multiphoton microwave spectroscopy [PRA 55, 3746 (1997)].

While this model building has assisted important experimental efforts, it has also underscored the need for a more fundamental and satisfying theoretical approach to the problem of long-range interactions. Important progress in this regard was reported in a 1996 article by Joseph Macek and Serge Ovchinnikov of the University of Tennessee and Oak Ridge National Laboratory [PRA 54, 544 (1996)]. Conceptually, these researchers likened the problems posed by an infinite number of rearrangement channels to Zeno's paradox and presented an elementary recipe for proceeding beyond infinity! In essence, while there are an infinite number of target states in a small energy interval, an infinite number of basis functions are not required to represent them. Macek and Ovchinnikov demonstrated that an infinity of target states can be represented, in a suitable reciprical space, by a single (Sturmian) function. Intrigued by this idea, I collaborated with Joseph Macek to illustrate and clarify the theory using a standard (Demkov-Osherov) model of ion-atom collisions [PRA 58 348(1998)]. More recently, I have reformulated this approach using renormalization techniques in order to calculate the excitation and ionization of Rydberg atoms by slow electrons. This latter effort is intended, once again, to complement a new experimental program in MacAdam's group, for which joint funding has been provided by the National Science Foundation.

I mentioned above that molecular dissociation is most often governed by long-range dispersion forces between neutral atoms. However, long-range Coulomb interactions can also play an important role when ion-pair formation channels are present, particularly in the breaking of ionic bonds. Urged by Hossein Sadeghpour of the Harvard-Smithsonian Center for Astrophysics (CfA), I have studied predissociating resonances of alkali-halide salts along with a graduate student in my group, Sean Cornett. Sean's thesis work predicted and interpreted an interferometric lineshape modulation of Rydberg series of predissociating resonances in alkali-halide photodissociation [PRL 82, 2488 (1999)]. Unlike autoionizing Rydberg levels in atoms, the heavy mass and long-range (tunneling) interactions between oppositely charged ion fragments of a dissociating molecule result in a beautiful and delicate spectrum of predissociating resonances. This work led to a sequence of collaborative papers with Sadeghpour and coworkers at the CfA and with a Quantum Chemistry group in Wuppertal, Germany [PRA 60, 1407(1999), JCP 113, 1514(2000)]. Two additional papers resulting from this effort are in progress.

Finally, interest in threshold phenomena associated with ultracold atoms and molecules has led me to analyze the influence of dispersion forces on molecular fragmentation processes. A new approach to this problem has been completed and a manuscript is in preparation. That part of the analysis that is relevant to threshold laws has already appeared in a recent review article [JPB 33, R93 (2000)].

In summary, my research interests are focussed on the development of new theoretical techniques for the treatment of long-range interactions between atoms and molecules and their fragment particles and ions. These efforts are firmly grounded by the practical demands of an in-house collaboration with experimental colleagues, but are potentially applicable to a wide array of phenomena in Atomic, Molecular and Optical physics.