Semiclassical Approach to the Scattering of Atomic Beams by a Corrugated Surface Potential: An Approximate Analytical Solution

An approximate analytic solution to the scattering problem of atoms by a weakly corrugated Morse potential is presented. In the classical limit the resulting scattering amplitude coincides with that given by the Kirchhoff approximation for the corrugated hard-wall model with a corrugation function identical to that of the Morse potential. Quantum mechanical effects appear as deviations from the Kirchhoff formula. For a general potential it is shown that it is the potential corrugation near vanishing potential which dominates the scattering process and not that at the classical turning point.