Debye-Waller factor in atom-surface scattering: Elastic and inelastic channels

Abstract Explicit expressions for the Debye-Waller factor for the elastic and one-phonon channels are presented to lowest order in the phonon displacement, using a hard wall model to represent the atom-surface interaction. The periodicity of the crystal is accounted for; thus we explicitly generalize to all elastic channels the reflectance result found by Garcia et al. within the plane-surface model, and we include the contribution of the umklapp processes to the inelastic channels. We show how for high incident energy of the atom all Debye-Waller factors reduce to the standard result.