Casimir Surface Force on a Dilute Dielectric Ball

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-1) (n being the refractive index) as a small parameter. The dispersive properties of the material are taken into account by adopting a simple dispersion relation, involving a sharp high frequency cutoff at omega = omega_0. For a nondispersive medium there appears (after regularization) a finite, physical, force F^{nondisp} which is repulsive. By means of a uniform asymptotic expansion of the Riccati-Bessel functions we calculate F^{nondisp} up to the fourth order in 1/nu. For a dispersive medium the main part of the force F^{disp} is also repulsive. The dominant term in F^{disp} is proportional to (n-1)^2{omega_0}^3/a, and will under usual physical conditions outweigh F^{nondisp} by several orders of magnitude.