CASIMIR FORCE ON A SPHERICAL-SHELL WHEN EPSILON(OMEGA)MU(OMEGA)=1

The Casimir surface force on a spherical shell is calculated, assuming the material to be satisfying the condition ε(ω)μ(ω) = 1, ε(ω) being the spectral permittivity and μ(ω) the spectral permeability. The basic formula for the force is given under general conditions, without any restrictive assumption on the thickness of the shell or on the specific dispersion relation. When it comes to numerical evaluations, it is assumed that the shell is of small thickness, and also that the simple form μ(ω) = μs(ω≤ω0), μ(ω) = 1 (ω>ω0), for the dispersion relation. The special case when μs → ∞ or 0 is given particular attention, since this case appears to be of main physical interest and also since it implies mathematical simplifications. The force ℱ may then be written as the sum of two terms: one "normal" term ℱ(0) containing an attractive dispersion-induced part as well as a repulsive, nondispersive finite part, and one "abnormal" term ℱ(1) that becomes divergent when summed over all angular momenta. This particular behavior of ℱ(1) is a consequence of the assumed small magnitude of the shell thickness. A similar analysis of the opposite extreme case of dilute media is also made, and analogous angular moment divergent results are found. The extraction of physically meaningful information from the divergent expressions is discussed. In general, numerical methods are necessary to handle the Riccati-Bessel functions, although in the special cases mentioned, useful analytic results are obtained using the Debye expansion. The numerical calculation of the Casimir force on shells of finite thickness is also commented upon, and in the Appendix the generalization of the theory to the case of finite temperatures is discussed. © 1990 American Institute of Physics.