Casimir surface force on a dilute dielectric ball

Abstract

The Casimir surface force density F on a dielectric dilute spherical ball of radius a, surrounded by a vacuum, is calculated at zero temperature. We treat $(n\ensuremath{-}1)(n$ being the refractive index) as a small parameter. The dispersive properties of the material are taken into account by adopting a simple model for the dispersion relation, involving a sharp high frequency cutoff at $\ensuremath{\omega}={\ensuremath{\omega}}_{0}.$ For a nondispersive medium there appears (after regularization) a finite, physical force ${F}^{\mathrm{nondisp}}$ which is repulsive. By means of a uniform asymptotic expansion of the Riccati-Bessel functions we calculate ${F}^{\mathrm{nondisp}}$ up to the fourth order in $1/\ensuremath{\nu}.$ For a dispersive medium the main part of the force ${F}^{\mathrm{disp}}$ is also repulsive. The dominant term in ${F}^{\mathrm{disp}}$ is proportional to $(n\ensuremath{-}{1)}^{2}{\ensuremath{\omega}}_{0}^{3}/a,$ and will under usual physical conditions outweigh ${F}^{\mathrm{nondisp}}$ by several orders of magnitude.