Scattering-theoretical approaches to multiphoton ionization in strong fields.

Abstract

The nonrelativistic version of the authors' theory of multiphoton ionization [Phys. Rev. 40, 4997 (1989)] is compared with other forms of scattering-theoretical approaches that employ different boundary conditions. These methods, which are expressed in terms of formal time-independent scattering theory, are shown to be equivalent in the large-photon-number limit to use of the semiclassical time-dependent S-matrix theory. In the authors' treatment it is assumed that the photoelectron has escaped from both the electromagnetic and atomic fields; a perturbation expansion in the photon-electron interaction is obtained that correctly accounts for the atomic final-state interactions of the photoelectron. The case of multiphoton detachment of ${\mathrm{I}}^{\mathrm{\ensuremath{-}}}$ is treated, for which the influence of the final-state atomic potential on the transition rate can be ignored. It is shown both analytically and numerically for the Nd--yttrium aluminum garnet wavelength that the transition rates obtained for this case from the various approaches are distinctly different. The present approach is shown to be consistent with an abrupt switching off of a spatially unlimited monomode field, in contrast with Keldysh-type approaches, which correspond to a long switch-off time if the ad hoc assumption of ponderomotive acceleration is made. Above-threshold-ionization spectra calculated from the present approach exhibit interference effects and are redshifted with respect to what is expected for slow switch-off. It is demonstrated, using the semiclassical time-dependent approach, that the corresponding final off-field scattering-state wave function only exists if the ponderomotive potential per unit photon energy is an integer, in accordance with our earlier time-independent analysis. The origin of this curious feature is made clear.