On the polarizability potential for two spheres

The appropriate transmission problem for the vector potential through which the General Polarizability Tensor is defined, is solved analytically in the case of two spheres embedded in an infinite medium. The spheres can be of different radii but are not allowed to touch each other. The potential problem is solved by employing the bispherical system of coordinates in which Laplace’s equation is R-separable. The vector potential is then expressed as a series expansion of exponentials, Legendre and trigonometric functions. The calculation of the exact solution leads to an infinite linear system, which can be solved approximately within any order of accuracy, through a cut-off procedure. Furthermore, the effect on the accuracy of the variation of the radii ratio and of the relative position of the spheres is investigated.