Quantum versus semiclassical treatment of multiphonon effects in He-atom scattering from surfaces

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Abstract
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).