Casimir energy and realistic model of dilute dielectric ball

The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically for the first time for an arbitrary physically possible frequency dispersion of dielectric permittivity $ϵ(i\omega )$. A microscopic model of dielectrics is considered, divergences are absent in calculations because an average interatomic distance $\lambda$ is a {\it physical} cut-off in the theory. This fact has been overlooked before, which led to divergences in various macroscopic approaches to the Casimir energy of connected dielectrics.