A manifestly gauge-invariant description of interaction of atomic systems with strong fields in the dipole approximation

Abstract: We propose a new type of gauge-invariant expansion of the ionization probability amplitudes of atoms by short pulses of electromagnetic radiation. Contrary to previous gauge-invariant approaches to this problem it does not require different partitions of the total Hamiltonian depending on the choice of gauge. In a natural way the atomic potential is treated as perturbation acting on an electron interacting with strong pulse. Whereas this is a standard assumption of strong field approximation (SFA), we show that grouping consequently together \textit{all} terms of the same order in the atomic potential results in the expansion of the amplitude which is gauge invariant \textit{order by order}, and not only in the limit of infinite series. In this approach, which is illustrated by numerical examples, the "direct ionization" and "rescattering" contributions are different from those commonly used in SFA - calculations.