Semiclassical treatment of two-center electron-electron interactions in energetic atomic collisions: Screening effects

The impact-parameter dependence of electronic screening effects is investigated within the framework of the time-dependent semiclassical perturbation theory concerning excitations. A multipole expansion is used for different screening potentials to determine time-dependent matrix elements which are suitable for first- or higher-order impact-parameter calculations. For numerical matrix elements, the present method provides a complete solution. Analytical formulas for 1s-2s and 1s-2p excitations are obtained by using hydrogenic wave functions. Our integrated cross sections are equivalent to those determined within the framework of the plane-wave Born approximation. It is shown that difficulties may arise in reproducing the present results by means of existing approximate factorization and scaling formulas