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 quasistatic 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. DOI: 10.1103/PhysRevA.87.012504