Theories for the effective polarizability of a small particle in a medium are presented using different levels of approximation: we consider the virtual cavity, real cavity, and the hard-sphere models as well as a continuous interpolation of the latter two. We present the respective hard-sphere and cavity radii as obtained from density-functional simulations as well as the resulting effective polarizabilities at discrete Matsubara frequencies. This enables us to account for macroscopic media in van der Waals interactions between molecules in water and their Casimir-Polder interaction with an interface.
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