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

Abstract

An expression for the partial frequency redistribution (PRD) matrix for line scattering in a twoterm 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 interferencenamely 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 an L = 0 → 1 → 0 scattering transition with S = 1/2 (a hypothetical doublet centered at 5000Å and 5001Å). 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.

The transfer of resonance line polarization with partial frequency redistribution andJ-state interference

“…This assumption is ultimately due to the fact that our R III has been derived in a heuristic way starting from the theory of LL04, which is based on the flat-spectrum approximation. Although other approximate forms of R III , based on different hypotheses, can in principle be proposed (see, for example, Smitha et al 2013), we believe that the theory of LL04 is at the moment the most robust one for deriving this redistribution matrix. A comparison between the different expressions of R III that have been proposed up to now, and a detailed analysis of their properties and weaknesses will be the object of a forthcoming paper.…”

Frequency Redistribution Function for the Polarized Two-Term Atom

“…This assumption corresponds to the hypothesis of non-coherent lower term (see Sect 3). More recently, Stenflo (1994) followed a heuristic approach built upon the Kramers-Heisenberg scattering amplitude in order to derive a semi-classical theory of partial redistribution, which has enabled the derivation of redistribution functions similar to those presented in this paper (see, e.g., Smitha et al 2013), again for atoms with non-coherent lower term.…”

Polarized Light Scattering With the Paschen-Back Effect, Level-Crossing of Fine Structure States, and Partial Frequency Redistribution

“…Assuming CRD, Casini & Manso Sainz (2005) considered the problem of PBE in a multi-term atom involving the interferences among both J and F states. In the linear Zeeman regime, where the fine structure splitting is larger than the splitting produced by the magnetic field, Smitha et al (2011Smitha et al ( , 2013 developed a theory for interference between the fine structure states taking into account the effects of PRD. In the present paper, we generalize the collisionless redistribution matrix (hereafter RM) derived by Smitha et al (2011) to include the PBE.…”