Emeritus Faculty

Scattering Theory; Theoretical Atomic, Molecular, and Many-body Physics

	Office 437 Phone (212) 998-7854 Mailing Address 4 Washington Place New York, NY 10003 Mail Box 058

Research The area of research is the theory of atomic structure and scattering processes. Applications have been made recently to the problem of electron-atom scattering in a laser field and to closely related problems dealing with the emission of soft photons during the scattering process. A major effort has gone into studies of the special effects associated with long-range interactions as well as the development of minimum principles for relativistic and nonrelativistic systems. Some recent publications are briefly described below. The effect of a low-frequency laser field on photoionization and radiative recombination processes was studied theoretically, accounting for the combined influence of the electron-ion Coulomb interaction and the laser field on continuum states of the system. A simple model, based on parametrizations of the type used in quantum-defect theory, was employed in a numerical study of the modification of resonant structures in the cross section induced by the external field. An effective-potential formalism, previously developed for electron scattering by a neutral target, was extended to apply to electron-ion scattering, with the requirement of antisymmetrization now accounted for explicitly. A minimum principle for the effective potential was derived, valid for scattering below the ionization threshold and applicable when, as is usually the case, the target wave functions are imprecisely known. Levinson's theorem relates the zero-energy phase shift for potential scattering in a given partial wave, by a spherically symmetric potential that falls off sufficiently rapidly, to the number of bound states of that angular momentum supported by the potential. An extension of this theorem was derived that applies to single-channel scattering of an electron by a neutral atom with the target initially in its ground state. The extended theorem differs from that derived for potential scattering; even in the absence of composite bound states the zero-energy phase shift may differ from zero as a consequence of the Pauli principle. In addition to a knowledge of the number of composite bound states, information (which can be rather incomplete) concerning the structure of the target ground-state wave function is required for an explicit, absolute determination of the phase shift. A systematic treatment of near-threshold electron-atom scattering based on a variational principle has been presented. Results extend the modified effective-range theory derived some time ago (in which long-range polarization forces are taken into account) by providing a prescription, based on a minimum principle, for calculating the effective range parameters.

Publications L. Rosenberg, "Effect of a laser field on resonant photoionization and recombination processes," Phys. Rev. A 51, 3676 (1995). L. Rosenberg, "Bound-state methods for low-energy electron-ion scattering," Phys. Rev. A 53, 791 (1996). L. Rosenberg and L. Spruch, "Generalized Levinson theorem: Applications to electron-atom scattering," Phys. Rev. A 54, 4985 (1996). L. Rosenberg, "Effect of long-range interactions on low-energy scattering parameters: Variational formulation," Phys. Rev. A 55, 2857 (1997).