Classical Casimir free energy for two Drude spheres of arbitrary radii: A plane-wave approach

We derive an exact analytic expression for the high-temperature limit of Casimir interaction between two Drude spheres arbitrary radii. Specifically, we determine free energy by using scattering approach in plane-wave basis. Within a round-trip expansion, are led to consider combinatorics certain partitions round trips. The relation and capacitance matrix is discussed. Previously known results special cases sphere-plane geometry as well equal radii recovered. An asymptotic expansion small distances determined analytical expressions coefficients given.