Analytical models of single phonon atom-surface diffractive scattering

Simple analytical (semiclassical) models of diffractive single phonon atom- surface scattering are presented. Within the approach applied, the inelasti c scattering amplitudes are expressed through the elastic ones which leads to the natural extension of the well-known Bessel approximation to inelasti c (single phonon) scattering. The expression for the probability of diffrac tive scattering derived in this work gives the correct description of inela stic scattering via umklapp processes accompanied by considerable parallel momentum transfer. This model does not suffer from nonphysical discontinuit ies at the edges of the surface Brillouin zone as confirmed by calculations of the single phonon diffractive scattering intensities for the He-Cu(110) system. Results of the comparison of the standard distorted-wave Born appr oximation with the semiclassical approach (generalized eikonal method) used in this work are also presented. II is shown that application of the semic lassical approach to the scattering problem requires the momentum formulati on of quantum mechanics to describe correctly the contribution of the vicin ity of the classical turning point to the semiclassical matrix element. (C) 2000 Elsevier Science B.V. All rights reserved.