Second Born treatment of multiphoton free-free transitions

Abstract

The Born series of charged-particle scattering in the presence of a strong radiation field is reconsidered with two specific aims: first, to provide a criterion of validity of the first Born approximation (FBA) appropriate to the case when the presence of the radiation field is taken into account; secondly, to perform exact numerical calculations of differential cross sections in the second Born approximation (SBA). Both items have never been considered before. The authors show that when the classical oscillatory velocity of the scattered particle is comparable to or larger than its translational velocity, the FBA enlarges its range of validity, particularly for long-range potentials. The SBA differential cross sections for radiation fields of intermediate strengths show significant modifications in both form and absolute values compared with the corresponding results in FBA. Comparisons with the Kroll-Watson approximation (KWA) are also presented, showing that for long-range potentials and small scattering angles the KWA fits the exact calculations poorly.