Eikonal Method in Atomic Collisions. I

Abstract

A complete and systematic quantal description of atomic collisions is developed employing the eikonal method. The lowest-order approximation involves the solution of the time-dependent Schrödinger equation for the electrons in the rectilinear trajectories of the atomic nuclei. The differential scattering amplitude (and hence the differential cross section) for the various reaction channels is expressed as a Fraunhofer integral, over the impact parameter, of the asymptotic state amplitudes. This completely avoids the ambiguities involved in obtaining an effective interatomic potential. Higher-order corrections are exhibited. However, the lowest-order approximation not only is valid at high energies, but penetrates deeply into the adiabatic regime, probably down to 100 eV. Numerical calculations will be presented in a later paper.