On the Zel'dovich regularization method in the theory of quasistationary states

Complex quasienergy and level width are calculated for a weakly bound atomic state in an intense circularly polarized monochromatic laser field using the method suggested by Zel'dovich for the regularization of divergent integrals with the Gamow wave function. It is demonstrated that this method converges, and the conditions for its applicability are indicated. These results are used to discuss the accuracy of the semiclassical approximation in the problems of ionization theory.