Validity of the Semiclassical Method for the Coupled-Channel Atomic Scattering Problem

Abstract

The $S$-matrix elements for the two-channel atomic scattering system are not smoothly varying functions; hence some justification must be given for the application of the stationary-phase approximation to the evaluation of scattering amplitudes for this system. For a specific example, we show that the contribution to the amplitudes from the region of rapid variation is negligible compared to the stationary-phase value, since the region of rapid variation is small and the phases vary sufficiently slowly. The semiclassical interpretation of the oscillations in the elastic and inelastic cross sections as the "interference" between two classical trajectories is therefore a valid one.