Ionization by an intense slowly varying laser field: Gauge-invariant approximations.

Abstract

A method to calculate amplitudes for ionization in a strong laser field is developed that is constrained in such a way that gauge invariance is necessarily satisfied when approximations are introduced. A variational approximation procedure is adopted here, in the context of a simplified model of a charged particle bound in a short-range potential. The physical situation considered in an illustration of the method is one in which the external field is slowly varying relative to the time required for the particle to penetrate the potential barrier. The approximation derived here represents an extension of results obtained previously for problems of this type in that the effect of the laser field on the propagation of the particle during the ionization process is accounted for, in a manner consistent with the assumed slowly varying nature of the field. This is accomplished, specifically, through the replacement of the unperturbed propagator in the integral equation defining the continuum (momentum-space) wave function of the particle in the potential by a generalized Airy function. The relation between the approximation derived here and some results obtained previously is briefly discussed.