Linear vs. nonlinear coupling effects in single- and multi-phonon atom-surface scattering

We present a comparative assessment of the features of inelastic atom-surface scattering spectra that are produced by several different forms of linear and nonlinear phonon coupling to the projectile atom. Starting from a simple theoretical model of atom-surface scattering and employing several recently developed exact numerical and approximate analytical methods we calculate and compare the scattering probabilities ensuing from each form of interaction and from each calculational scheme. This enables us to demonstrate that in the regime of thermal energy atom scattering from surfaces the dominant contributions to the zero-, one- and multi-phonon excitation probabilities obeying unitarity arise from linear coupling treated to all orders in the interaction.