A Unifying Polarization Formalism for Electric and Magnetic Multipole Interactions

We extend the spherical tensorial formalism for polarization to the treatment of electric- and magnetic-multipole transitions of any order. We rely on the spherical-wave expansion to derive the tensor form of the operator describing the interaction of the atomic system with a polarized radiation field, which naturally leads to the introduction of spherical tensors describing the polarization properties of the interacting field. As a direct application, the formalism is used to model the radiation anisotropy affecting the scattering of radiation in an electric-quadrupole transition, and the associated Hanle effect in the presence of a magnetic field.