Configuration-space methods for Coulomb scattering in a laser field.

Abstract

The Volkov wave function describing the motion of a charged particle in a laser field serves as a modified plane wave in the formulation of external-field collision theory and is widely used in applications. Exact solutions are unavailable for those cases in which the target, as well as the projectile, carries a net charge. It is shown that this difficulty may be overcome through the adoption of a variational formulation of the theory in configuration space. The essential feature of this procedure is the specification of boundary conditions to be satisfied by the trial functions whereby the combined effect of the Coulomb potential and the external field is accounted for with sufficient accuracy. Wave packets constructed from such trial functions satisfy the physical requirement that they follow classical trajectories at asymptotic times. The formalism is applied to the problem of potential scattering in a low-frequency external field and leads to an approximate transition amplitude that serves as a generalization of the Kroll-Watson approximation, reducing to it for potentials having no long-range Coulomb tail. In addition, a relatively simple Coulomb generalization of the cross-section sum rule is obtained. As a second application a low-frequency approximation is derived for the amplitude for laser-assisted electron-impact ionization. It is based on a choice of trial functions that accounts for the effect on the asymptotic motion of these particles of the long-range final-state Coulomb interactions among pairs of charged particles, in the presence of the laser field. The applicability of this approach to multiphoton-ionization processes is discussed briefly.