High-multipolar effects on the Casimir force: The non-retarded limit

We implement a spectral representation formalism to calculate exactly the non-retarded Casimir force or dispersive van der Waals force, between a spherical nanoparticle and a planar substrate beyond the dipolar approximation. For a sphere of radius R separated a distance z from the substrate, we find that high-order multipole interactions induce extra factors R/z in the force, as compared to the dipole power law of ∼ R3/z3. As a consequence, at small separations the non-retarded Casimir force increases by several orders of magnitude with respect to that estimated in the usual dipole approximation.