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Fluctuation induced forces are a hallmark of the interplay of fluctuationsand geometry. We recently proved the existence of a multi-parametric family ofexact representations of Casimir and Casimir-Polder interactions between bodiesof arbitrary shape and material composition, admitting a multiple scatteringexpansion (MSE) as a sequence of inter- and intra-body multiple wavescatterings [G. Bimonte, T. Emig, Phys. Rev. A 108, 052807 (2023)]. Theapproach requires no knowledge of the scattering amplitude (T-matrix) of thebodies. Here we investigate the convergence properties of the MSE for theCasimir-Polder interaction of a polarizable particle with a macroscopic body.We consider representative materials from different classes, such asinsulators, conductors and semiconductors. Using a sphere and a cylinder asbenchmarks, we demonstrate that the MSE can be used to efficiently andaccurately compute the Casimir-Polder interaction for bodies with smoothsurfaces.

Surface Scattering Expansion of the Casimir-Polder Interaction for  Magneto-dielectric Bodies: Convergence Properties for Insulators, Conductors  and Semiconductors