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 ioniza
tion which accommodates both the above-threshold ionization peaks and
atomic resonances. The lowest-order term in the expansion yields the u
sual Keldysh approximation if the final state is replaced by a plane w
ave. We show that, even though this term is not reliable in general, i
t may produce an excellent agreement with the exact result for a three
-dimensional zero-range potential and a circularly polarized field. Fo
r this situation, we calculate exactly the next nonvanishing term in t
he expansion, and establish precisely the conditions under which it ca
n be neglected.