QUANTUM VERSUS SEMICLASSICAL TREATMENT OF MULTIPHONON EFFECTS IN HE-ATOM SCATTERING FROM SURFACES

We develop a formalism appropriate for studying multiple inelastic sca ttering of thermal-energy He atoms from surface phonons in the collisi on regimes in which both the motion of the particle and surface vibrat ions must be treated quantum mechanically. Having in mind recent exper iments on He-atom scattering (HAS) from surfaces, we first point out s ome difficulties connected with calculating the reflection coefficient s under extreme multiphonon conditions by resorting to the standard T- matrix approach. To circumvent these problems we make use of the conne ction between the reflection coefficients and angular resolved scatter ing spectra and show how the latter can be conveniently obtained in th e form of a cumulant expansion for multiphonon-scattering amplitudes i n powers of inelastic atom-surface coupling. This yields the expressio n for the scattering spectrum whose advantageous characteristics are t he unitarity (which manifests itself through a Debye-Waller factor in exponential form with a complete Debye-Waller exponent encompassing co ntributions from all inelastic scattering channels) and the amenabilit y to perturbational treatment in terms of uncorrelated and correlated atom-phonon interactions. In the scattering regimes in which the contr ibutions of correlated multiphonon excitations become negligible relat ive to those of uncorrelated ones, the scattering spectrum acquires a particularly simple form of an exponentiated Born approximation (EBA). As various other semiclassical and classical approximations regarding the particle dynamics can be shown to emerge from the EBA, we estimat e its validity for treating multiple He-atom scattering by Einstein- a nd Debye-like phonons in representative collision systems He-->CO(root 3 X root 3)R 30 degrees/Rh(111) and He-->Cu(001) in which such modes have been experimentally detected. We find that under the conditions o f these experiments the EBA can be considered as exact, which enables accurate calculation of the corresponding multiphonon-scattering spect ra. The obtained results compare well with experimental data, thereby confirming the potentiality and applicability of the developed formali sm in HAS. We also show that the semiclassical trajectory and fast col lision or impulse approximations, which naturally derive as special li mits of the EBA, can largely deviate from the so-defined exact EBA tre atment in the considered range of the parameter space. From this we co nclude that they may become unreliable in the scattering regimes in wh ich either the validity of the EBA is violated or their deviation from the EBA is large.