Shortcomings of the Keldysh approximation

A simple derivation of the Keldysh amplitude for the ionization of an atom by a strong field is presented using a perturbation expansion in the binding potential. It is shown that the ''Keldysh approximation'' is questionable under conditions of strong ionization, when there is substantial probability of removing the electron from its initial bound state. This is consistent with published numerical studies based on model binding potentials. It is argued that the Keldysh amplitude is not gauge invariant in the usual sense, and that it is effectively canceled in a conventional gauge-invariant formulation of strong-field perturbation theory