We give an exact series expansion of the Casimir force between plane and spherical metallic surfaces in the non trivial situation where the sphere radius R, the plane-sphere distance L and the plasma wavelength λP have arbitrary relative values. We then present numerical evaluation of this expansion for not too small values of L/R. For metallic nanospheres where R, L and λP have comparable values, we interpret our results in terms of a correlation between the effects of geometry beyond the proximity force approximation (PFA) and of finite reflectivity due to material properties. We also discuss the interest of our results for the current Casimir experiments performed with spheres of large radius R ≫ L.The Casimir force is a striking macroscopic effect of quantum vacuum fluctuations which has been seen in a number of dedicated experiments in the last decade (see for example [1,2] and references therein). One aim of the Casimir force experiments is to investigate the presence of hypothetical weak forces predicted by unification models through a careful comparison of the measurements with quantum electrodynamics predictions. This aim can only be reached if theoretical computations are able to take into account a realistic and reliable modeling of the experimental conditions. Among the effects to be taken into account are the material properties and the surface geometry, these effects being also able to produce phenomena of interest in nanosystems [3,4].A number of Casimir measurements have been performed with gold-covered plane and spherical surfaces separated by distances L of the order of the plasma wavelength (λ P ≃ 136nm for gold), making material properties important in their analysis [5]. As those measurements use spheres with a radius R ≫ L, they are commonly analyzed through the Proximity Force Approximation (PFA) [6], which amounts to a trivial integration over the sphere-plate distances. An exception is the Purdue experiment dedicated to the investigation of the accuracy of PFA in the sphere-plate geometry [7], the result of which will be given as a precise statement below.In the present letter, we give for the first time an exact series expansion of the Casimir force between a plane and a sphere in electromagnetic vacuum, taking into account the material properties via the plasma model (see Fig. 1). We present numerical evaluation of this expansion which are limited to not too small values of L/R, because of the multipolar nature of the series. We show below that these new results lead to a striking correlation between the effects of geometry and imperfect reflection when evaluated for nanospheres, with R, L and λ P having comparable values. In the end of this letter, we also discuss the interest of these results for the Casimir experiments performed with large spheres R ≫ L [7].Our starting point is a general scattering formula for the Casimir energy [8]. Using suitable plane-wave and multipole bases, we deduce the Casimir energy E PS be- tween a plane and a spherical metallic surface in electromagnetic...

In this paper we calculate the Casimir energy for a dielectric-diamagnetic cylinder with the speed of light differing on the inside and outside. Although the result is in general divergent, special cases are meaningful. The well-known results for a uniform speed of light are reproduced. The self-stress on a purely dielectric cylinder is shown to vanish through second order in the deviation of the permittivity from its vacuum value, in agreement with the result calculated from the sum of van der Waals forces. These results are unambiguously separated from divergent terms.

The local Casimir energy density and the global Casimir energy for a massless scalar field associated with a λδ-function potential in a 3+1 dimensional circular cylindrical geometry are considered. The global energy is examined for both weak and strong coupling, the latter being the well-studied Dirichlet cylinder case. For weak-coupling, through O(λ 2 ), the total energy is shown to vanish by both analytic and numerical arguments, based both on Green's-function and zeta-function techniques. Divergences occurring in the calculation are shown to be absorbable by renormalization of physical parameters of the model. The global energy may be obtained by integrating the local energy density only when the latter is supplemented by an energy term residing precisely on the surface of the cylinder. The latter is identified as the integrated local energy density of the cylindrical shell when the latter is physically expanded to have finite thickness. Inside and outside the δ-function shell, the local energy density diverges as the surface of the shell is approached; the divergence is weakest when the conformal stress tensor is used to define the energy density. A real global divergence first occurs in O(λ 3 ), as anticipated, but the proof is supplied here for the first time; this divergence is entirely associated with the surface energy, and does not reflect divergences in the local energy density as the surface is approached.