Spectral representation of the nonretarded dispersive force between a sphere and a substrate

We develop a spectral representation formalism to calculate the nonretarded Casimir force between a spherical particle and a substrate, both with arbitrary local dielectric properties. The spectral formalism allows us to study systematically such force as a function of its geometrical properties separately from its dielectric properties. The calculated force is attractive, and at a small separations it is orders of magnitude larger for nanometric-size spheres than for micrometer particles. We also found that the force depends more on the dielectric properties of the sphere than of the substrate.