Thermal Casimir effect for Drude metals in the plane-sphere geometry

We compute the Casimir interaction between a plane and a sphere, the configuration employed in the most precise experiments. The scattering formula is developed by taking a suitably chosen plane-wave and multipole basis and is valid for arbitrary values of the sphere radius, interplate distance, temperature, and arbitrary dielectric functions for both sphere and plate. Our analytical and numerical results for metallic surfaces show a nontrivial interplay between the effects of curvature, temperature, finite conductivity, and dissipation.