We present an alternative approach to analyze atomic behavior when an external field perturbation is not sudden for a number of states of the field-free system. It is shown that the probability amplitudes for the system to be in these states can be accurately estimated from the closed set of their integral equations. Numerical examples for an electron in a one-dimensional Coulomb potential interacting with (i) laser and (ii) half-cycle pulses are provided. Comparison with exact calculations indicates the strength of the approach.

• Received 23 October 2007

DOI:https://doi.org/10.1103/PhysRevA.77.023420