APJ: We extend the spherical tensorial formalism for polarization to the treatment of eletric- 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.
Hanle diagrams for the 90-deg scattering of resonant radiation in the E2 transition (Jl , Ju) = (0, 2) (top row) and in the E1 transition (Jl , Ju)=(0, 1) (bottom row). Two inclinations (30 deg and 90 deg) of the magnetic field from the local vertical are shown (respectively two leftmost and two rightmost panels). Each curve spans a range of magnetic Larmor frequencies, normalized by the inverse lifetime of the excited level, between 0.1 and 10 (range of criticality of the Hanle effect). Each colored curve is for different field azimuths ranging from -180 to +150 deg in steps of 30 deg.