Retarded and nonretarded van der Waals interactions between a cluster and a second cluster or a conducting surface

In some respects, a cluster consisting of many atoms may be regarded as a single large atom. Knowing the dielectric properties of such a cluster permits one to evaluate the form of the van der Waals ~dispersion! interactions between two clusters or between one cluster and a surface. In this paper, we derive these interactions in two extreme opposite regimes of separation: fully retarded and nonretarded. In the fully retarded regime ~very large separation!, the magnitude of the interaction is determined by just the static polarizability of the cluster~s!. In the nonretarded regime ~small separation!, we employ a single resonant frequency model of the cluster polarizability to derive expressions for the interactions’ coefficients. Numerical examples are presented to demonstrate that many-body screening of these interactions can be significant. The results represent the corrections to the commonly used approximation of pairwise additivity of interatomic interactions.