Coulomb-Volkov S-matrix theory of ionisation

In this paper we outline the recently derived Coulomb-Volkov (CV) S-matrix theory and present the results of calculations of the energy and the momentum spectra of the electrons emitted from ionisation of Ar atoms by an intense long-wavelength laser field. The results are compared with the corresponding calculations using the usual (plane-wave) SFA S-matrix theory, up to the second order of the series. We introduce a modified stationary phase method with a parametric integration to evaluate the high-dimensional integrals that occur in the second order of the ionisation amplitudes. The final-state Coulomb effect is found to be dominant at the lower energies, where the two theories differ greatly. In contrast, at high energies, the two theories produce qualitatively similar (in the logarithmic scale) distributions. It is found that despite the similarity of the positions of the 'forward rescattering' (or 'soft collision') peaks shown by the second order CV- and the SFA-amplitude, the line-shapes produced by them are qualitatively different. For example, the CV-spectrum shows a peak at 0.1 U _p with a characteristic line-shape that is convex on one side and steeply rising on the other side; this is qualitatively similar to the line-shape of the peak observed experimentally earlier at the same energy. In contrast, the SFA-spectrum shows at the same energy a pointed peak with a line-shape that is concave on both sides. The characteristic line-shape of the low energy LES-peak(s) thus appears to suggest itself as a signature of the final-state Coulomb interaction in strong-field ionisation processes. (paper)