Radiative correction in approximate treatments of electromagnetic scattering by point and body scatterers

The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the scattering matrix ($S$-matrix) used in quantum mechanics and quantum field theory. Focusing on electromagnetic scattering, we highlight an alternative formulation of the $T$-matrix approach, based on the use of the reactance matrix or $K$-matrix, which is more suited to formal studies of energy conservation constraints (such as the optical theorem). We show in particular that electrostatics or quasi-static approximations can be corrected within this framework to satisfy the energy conservation constraints associated with radiation. A general formula for such a radiative correction is explicitly obtained, and empirical expressions proposed in earlier studies are shown to be special cases of this general formula. This work therefore provides a justification of the empirical radiative correction to the dipolar polarizability and a generalization of this correction to any types of point or body scatterers of arbitrary shapes, including higher multipolar orders.