Classical theory for asymmetric in-plane atom surface scattering

In-plane atom surface scattering perturbation theory within a generalized Langevin equation formalism is proposed to account for the asymmetry found in angular distributions of heavy rare gas atoms scattered by corrugated surfaces. We show that when the surface corrugation is represented in terms of the first two (sine) Fourier components, one finds an asymmetric angular distribution. This asymmetry reflects the ratchetlike form of the effective corrugation. Adding in higher-order terms can also increase the number of rainbow scattering angles. Three rainbows are found for a second-order sine term in the corrugation, four symmetrically spaced rainbow angles are found when adding in a second-order cosine term to the corrugation. Analytic expressions for the angular distribution are derived in terms of a Morse oscillator model. The theory accounts well for the asymmetry and predicts its disappearance as the incident scattering angle is increased. It also features a decrease in the distance between the rainbow angles as the angle of incidence is increased and as the incident energy is increased. The theory is successfully applied to the experimental results of Kondo et al. [Eur. Phys. J. D 38, 129 (2006)] for the scattering of Ar on LiF(100) and the results of Amirav et al. [J. Chem. Phys. 87, 1796 (1987)] for the scattering of Xe on Ge(100) and Ar and Kr on Ag(100).