On the Strong-Field Approximation Describing Atoms and Molecules in Intense Laser Fields

A very popular theory to describe atomic (and recently also molecular) behavior in intense laser fields is the strong-field approximation (SFA), also known as Keldysh-Faisal-Reiss theory. It can be seen as the first-order term of an in principle exact time-dependent $S$-matrix theory. We have recently investigated some aspects of this theory in more detail. This includes the correctness of a recently proposed ``exact'' Keldysh theory based on the residue theorem instead of the saddle-point method. Furthermore, we have derived an analytical expression of the velocity-gauge SFA in the long-wavelength limit including the full Coulomb interaction. This revealed a break-down of the theory, but also allowed for a derivation of a new Coulomb correction factor and of a simplified quasi-static SFA (QSFA) that is of special interest for experimental studies in which the wavelength is scanned over large ranges. Finally, we will comment on a recently proposed SFA formulation in a ``gauge-invariant gauge.''