Classical Theory of Atom Scattering from Corrugated Surfaces

A theory based in the semiclassical eikonal approximation is developed to describe energy transfer in the collision of an atomic projectile with a surface which is either ordered or disordered. This theory is extended from the quantum mechanical regime to the classical regime of complete quantum decoherence via the Bohr correspondence principle of large numbers of excited quanta. In the quantum mechanical regime the theory reproduces the well-known eikonal approximation for elastic collisions, provides a simple and useful expression for single phonon inelastic scattering, and leads to further expressions for multiple phonon transfers. In the classical limit the theory produces an expression that includes the effects of surface corrugation in addition to the excitations of large numbers of phonons. This new theory shows that a simple measurement of the most probable intensity of energy-resolved scattering spectra taken as a function of surface temperature, with all other experimentally controllable parameters held fixed, can be used to extract the surface corrugation amplitude. Comparisons with data for Ar scattering from the molten metals Ga and In shows good agreement with the measured energy resolved spectra, the in-plane angular distributions, the out-of-plane angular distributions and produces values for the corrugation amplitudes that range from 10 to 30% of the average interparticle spacing.