  The fully retarded dispersion interaction between an atom and a cluster or
between two clusters is calculated. Results obtained with two different methods
are compared. One is to consider a cluster as a collection of many atoms and
evaluate the sum of two-body and three-body interatomic interactions, a common
assumption. The other method, valid at large separation, is to consider each
cluster as a point particle, characterized by a polarizability tensor, and
evaluate the inter-cluster interaction. This method employs the static
polarizability, evaluated by including all many-body (MB) intra-cluster atomic
interactions self-consistently, which yields the full inter-cluster
interaction, including all MB terms. A comparison of the results from the two
methods reveals that the contribution of the higher-than-three-body MB
interactions is always attractive and non-negligible, with a relative
importance that varies with geometry. The procedure is quite general and is
applicable to any shape or size of dielectric clusters, in principle. We
present numerical results for clusters composed of atoms with polarizability
consistent with silica, for which the higher-than-three-body MB correction term
can be as high as 42% of the atomic pair-wise sum. The full result is quite
sensitive to the anisotropic structure of the cluster, in contrast to the
result found in the additive case, which is orientation independent. We also
present a power law expansion of the total van der Waals (VDW) interaction as a
series of n-body interaction terms.
