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We propose a new type of gauge-invariant expansion of the ionizationprobability amplitudes of atoms by short pulses of electromagnetic radiation.Contrary to previous gauge-invariant approaches to this problem it does notrequire different partitions of the total Hamiltonian depending on the choiceof gauge. In a natural way the atomic potential is treated as perturbationacting on an electron interacting with strong pulse. Whereas this is a standardassumption of strong field approximation (SFA), we show that groupingconsequently together \textit{all} terms of the same order in the atomicpotential 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 thisapproach, which is illustrated by numerical examples, the "direct ionization"and "rescattering" contributions are different from those commonly used in SFA- calculations.

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