van der Waals interaction in atom-surface scattering

Corrections to the conventional dipole expression for the attractive interaction between an atom and a metal surface are calculated and discussed in several models: (i) the electrostatic image model, primarily used to define the multipole corrections and to give a simple, although accurate, estimate thereof; (ii) a model that includes both $s$ and $d$ electrons in the metallic dielectric response together with an atomic polarizability accounting for multipole contributions; and (iii) a model with a realistic treatment of the coupling between density fluctuations in the metal and on the atom (the conventional methods overestimate it). The models show what factors are needed to avoid a singular interaction at the dynamical image plane. While the point dipole of model (ii) allows polarization response at all wavelengths, and leads to singular behavior, model (iii) shows how the finite extent of the atom limits the ability of the system to respond to polarizing fields of short wavelengths. The latter "saturation" of the response competes with the multipole contributions and reduces their influence on the interaction potential over the whole range of distances, and leads to a finite potential also for shorter distances, where the saturation is particularly important. The models are illustrated with numerical calculations for helium on noble metals. With a proper description of the repulsive interaction the resulting physisorption potential is in agreement with experimental findings. We also apply our results for helium to give some brief comments for another interesting atom/substrate system: ${\mathrm{H}}_2$ on noble metals.