Applications of perturbation theory to atom–surface diffraction

Abstract

A model for atom–surface diffraction is treated by two perturbative schemes: the distorted wave Born series and the reaction matrix method. The first order reaction matrix calculation is identical to the approximate close coupling equations developed by CCGM for a potential with no bound states. Higher order perturbation terms are calculated numerically for a purely repulsive interaction potential. We find good agreement using both perturbative methods with Wolken’s exact close coupling calculations. The convergence of the distorted wave Born series is found to be best for small incident mass and low incoming energy. A similar perturbative treatment of the Rayleigh equation is applied to the atom‐surface diffraction problem with a hard corrugated surface potential. Results are compared to exact and semiclassical results. Improvements are found in the low energy region where errors are less than 0.1% in fourth order perturbation theory for specular diffraction and less than 1% in third order perturbation theory for first order diffraction events.