Single- and multiphonon atom–surface scattering in the quantum regime

Recent developments and achievements in the theoretical interpretation of inelastic scattering of thermal energy beams of He and other noble gas atoms from surfaces are reviewed, with a special emphasis on the successful interpretation of multiphonon He atom scattering (HAS) experiments. These developments have been stimulated by the remarkable successes of HAS time-of-flight spectroscopy in revealing information on the low-energy dynamics of the various surfaces, adlayers and isolated adsorbates. The diversity of the developed theoretical approaches reflects also the diversity of the various observables that have been assessed under the different experimental conditions. To aid the systematization and cross-correlation among the different model descriptions we first present a short outline of their characteristics and main achievements. Although many of these theories have been improved and refined in the course of time, a unified approach was required for a fully quantum treatment of elastic (diffractive or diffuse) and inelastic (single- and multiphonon) atom–surface scattering processes on an equivalent footing. A substantial progress towards this end has been made in recent years by going beyond the standard semiclassical and perturbation methods in the analyses of HAS experiments. The present review focuses on the development of one such approach based on the so-called scattering spectrum formalism in which the quantum scattering amplitudes are calculated by using cumulant or linked cluster expansion in terms of the correlated and uncorrelated scattering events. This formalism is equally well suited for making a passage to perturbative quantum-mechanical and nonperturbative semiclassical treatments of inelastic atom–surface scattering. Using the developed formalism we first establish the relevant approximations for calculating the scattering spectra and examine their validity for the scattering conditions typical of HAS. In the next step the formalism is applied to benchmark systems to interpret the scattering data which intermingledly depend on the vibrational dynamics of the investigated surfaces per se and on the projectile–surface interaction potentials. A very good agreement between experimental results and theoretical predictions for HAS from surfaces characteristic of the different types of surface vibrational dynamics is obtained in all studied scattering regimes. This demonstrates a broad applicability of the developed formalism in the interpretations of inelastic HAS experiments and in the assessments of phonon-mediated energy transfer in gas–surface collisions.