KELDYSH-LIKE EXPANSION FOR ABOVE-THRESHOLD IONIZATION

We develop a systematic expansion based on a semiclassical description of the ionized electrons for an atom subjected to a laser field. This expansion yields a transition amplitude for atomic multiphoton ionization which accommodates both the above-threshold ionization peaks and atomic resonances. The lowest-order term in the expansion yields the usual Keldysh approximation if the final state is replaced by a plane wave. We show that, even though this term is not reliable in general, it may produce an excellent agreement with the exact result for a three-dimensional zero-range potential and a circularly polarized field. For this situation, we calculate exactly the next nonvanishing term in the expansion, and establish precisely the conditions under which it can be neglected.