Casimir force on a solid ball when ε(ω)μ(ω)=1

The Casimir surface force on a solid ball is calculated, assuming the material to be dispersive and to be satisfying the condition ε(ω)μ(ω)=1, ε(ω) being the spectral permittivity and μ(ω) the spectral permeability. This particular condition simplifies the Casimir theory of dielectric media considerably. As a dispersion relation we choose the analogue of Sellmeir’s form (with one absorption frequency), known from ordinary dispersion theory. We follow a combined numerical and analytic approach: the low values of the angular momentum variable are treated numerically, whereas the higher values are treated analytically by means of the Debye expansion. The dispersive effect is found to yield a strong, attractive contribution to the surface force. If the cutoff frequency ${\omega }_0$ is large, the dispersion-induced surface force becomes proportional to ${\omega }_0$.