Polarized line formation with J-state interference in the presence of magnetic fields: A Heuristic treatment of collisional frequency redistribution

An expression for the partial frequency redistribution (PRD) matrix for line scattering in a two-term atom, which includes the J-state interference between its fine structure line components is derived. The influence of collisions (both elastic and inelastic) and an external magnetic field on the scattering process is taken into account. The lower term is assumed to be unpolarized and infinitely sharp. The linear Zeeman regime in which the Zeeman splitting is much smaller than the fine structure splitting is considered. The inelastic collision rates between the different levels are included in our treatment. We account for the depolarization caused by the collisions coupling the fine structure states of the upper term, but neglect the polarization transfer between the fine structure states. When the fine structure splitting goes to zero, we recover the redistribution matrix that represents the scattering on a two-level atom (which exhibits only m-state interference-namely the Hanle effect). The way in which the multipolar index of the scattering atom enters into the expression for the redistribution matrix through the collisional branching ratios is discussed. The properties of the redistribution matrix are explored for a single scattering process for a L=0→1→0 scattering transition with S=1/2 (a hypothetical doublet centered at 5000 Å and 5001 Å). Further, a method for solving the Hanle radiative transfer equation for a two-term atom in the presence of collisions, PRD, and J-state interference is developed. The Stokes profiles emerging from an isothermal constant property medium are computed.

► Polarized partial frequency redistribution matrix (PRDM) for two-term atom is derived. ► PRDM includes collisions heuristically and magnetic fields in linear Zeeman regime. ► A method to include this PRDM into the radiative transfer equation is presented. ► The transfer equation is solved both for the magnetic and non-magnetic cases. ► The Stokes profiles are computed for different models of the atmospheric slab.