Unified model of diffractive and multiphonon He atom scattering from adsorbates: Holstein renormalization of the interactions and the complete Debye-Waller factor

We derive general expressions for the energy and lateral momentum resolved scattering spectrum describing collisions of beams of thermal energy He ato ms with adsorbates on a flat substrate surface. Elastic and inelastic compo nents of the projectile-adlayer interaction, of which the latter can be non linear in adsorbate displacements, are treated to all powers in the couplin g constant g and with full account of the projectile recoil. The establishe d formalism enables a combined treatment of elastic scattering (either diff use or diffractive) and inelastic excitation of multiple phonons and overto nes in the adlayer on an equivalent footing. For nonlinear vibrational coup ling the distorted wave matrix elements of the interactions are Holstein-re normalized by zero point motion of adsorbates. In the case of scattering in tensities calculated to lowest order in g this gives rise to a direct analo g of the standard Glauber-van Hove Debye-Waller factor. The closed form sol utions for the scattering spectra to all orders in g are characterized by a unified or complete Debye-Waller factor which embodies the effects discuss ed so far only separately in the literature: (i) attenuation of the scatter ed beam intensities due to zero point motion of adsorbates, and (ii) attenu ation of the beam intensity in the elastic channel due to inelastic scatter ing from adlayer phonons and overtones. The complete Debye-Waller factor ac quires a form of an exponentiated sum of Holstein-renormalized scattering i ntensities and acts to preserve the unitarity of the scattering spectrum in accord with the optical theorem. The developed model facilitates evaluatio n of the various approximate and Limiting forms of the scattering spectra a nd the associated Debye-Waller factors characteristic of the different scat tering regimes and different types of adlayer vibrational dynamics. Potenti al applications of the model are illustrated by estimating the effect of Ho lstein renormalization occurring in the unified Debye-Waller factor and sca ttering intensities for several prototype adlayer systems. [S0163-1829(99)0 2428-5].