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

We develop a formalism appropriate for studying multiple inelastic scattering of thermal-energy He atoms from surface phonons in the collision regimes in which both the motion of the particle and surface vibrations must be treated quantum mechanically. Having in mind recent experiments on He-atom scattering (HAS) from surfaces, we first point out some difficulties connected with calculating the reflection coefficients under extreme multiphonon conditions by resorting to the standard T-matrix approach. To circumvent these problems we make use of the connection between the reflection coefficients and angular resolved scattering spectra and show how the latter can be conveniently obtained in the form of a cumulant expansion for multiphonon-scattering amplitudes in powers of inelastic atom-surface coupling. This yields the expression for the scattering spectrum whose advantageous characteristics are the unitarity (which manifests itself through a Debye-Waller factor in exponential form with a complete Debye-Waller exponent encompassing contributions from all inelastic scattering channels) and the amenability to perturbational treatment in terms of uncorrelated and correlated atom-phonon interactions. In the scattering regimes in which the contributions of correlated multiphonon excitations become negligible relative 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 estimate its validity for treating multiple He-atom scattering by Einstein- and 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 of these experiments the EBA can be considered as exact, which enables accurate calculation of the corresponding multiphonon-scattering spectra. The obtained results compare well with experimental data, thereby confirming the potentiality and applicability of the developed formalism in HAS. We also show that the semiclassical trajectory and fast collision or impulse approximations, which naturally derive as special limits of the EBA, can largely deviate from the so-defined exact EBA treatment in the considered range of the parameter space. From this we conclude that they may become unreliable in the scattering regimes in which either the validity of the EBA is violated or their deviation from the EBA is large.