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.