Hanle-Zeeman scattering matrix

A theory is presented that allows the Mueller matrix for coherent scattering to be calculated for arbitrary magnetic fields, atomic multiplets, and scattering transitions (Rayleigh or Raman scattering). For the special case of a normal Zeeman triplet (a J = 0 → 1 → 0 scattering transition) a compact analytical form for the scattering matrix is given, which allows us to better see how the various field-strength regimes are connected. A number of limiting cases are retrieved from the general theory, including the weak-field Hanle phase matrix, the polarization of forbidden coronal lines (strong-field limit), “thermal” radiation (emission vector in LTE) and incoherent scattering. The analytical form for the transition of the Hanle effect from the line core (where it is present) to the line wings (where it is absent) is given.