Mie-Type Calculation of the Generalized Electromagnetic Nonlocal Conductivity Tensor for a Sphere and Its Equivalence to the T-Matrix Operator

The purpose of this article is to calculate the generalized nonlocal conductivity tensor of a spherical particle made of isotropic and linear materials. The generalized conductivity tensor is a crucial element in the formulation of the mean-field theories of the electromagnetic response of random particulate systems. This is equivalent to what is called the T-Matrix in multiple scattering theories. Here, a new method is proposed for finding explicit expressions for this tensor directly from its definition including the magnetic response of the spheres. Its relation with the S-Matrix in the theory of single scattering is stated as a generalization. Several approximations and limit cases of possible interest in specific systems are analyzed and the results of some calculations are presented as a numerical example.