Simple theory of atom-surface scattering

The theory of the scattering of a beam of particles by a corrugated surface potential is shown to simplify dramatically in the semiclassical limit if the corrugation is not too strong and the direction of the incoming beam is close to the surface normal. It is shown that in any scattering event by a potential of quite general form the scattering amplitude is dominated by the potential corrugation near vanishing potential. For a weakly corrugated Morse potential, it is found that under near-normal-incidence conditions the classical scattering cross section is identical to the corresponding cross section for scattering by a hard corrugated wall with the same corrugation. Quantum-mechanical effects appear as small oscillations about the Kirchoff scattering amplitude. It is proposed that the observation of pronounced neon diffraction from Ni(110) and Pd(110), reported recently, may be reasonably explained if the corrugation function is defined at vanishing potential rather than at the classical turning points.