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 ω = ω0. For a nondispersive medium there appears (after regularization) a finite, physical, force Fnondisp which is repulsive. By means of a uniform asymptotic expansion of the RiccatiBessel functions we calculate Fnondisp up to the fourth order in 1/ν. 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)2ω3 0/a , and will under usual physical conditions outweigh Fnondisp by several orders of magnitude. Corresponding author. E-mail address: [email protected]