A Note on the Radiative and Collisional Branching Ratios in Polarized Radiation Transport with Coherent Scattering

TL;DR

This paper develops a physically consistent method to determine branching ratios between complete redistribution and partial redistribution contributions to polarized radiation emissivity, accounting for collisions and coherence effects.

Contribution

It introduces a new formulation for emissivity in polarized multi-term atoms, based on a diagrammatic analysis of radiative and collisional processes, improving the understanding of scattering in polarized radiation transport.

Findings

Derived an expression for emissivity combining CRD and PRD contributions.

Provided a heuristic diagrammatic approach to determine branching ratios.

Enhanced modeling of polarized radiation with collisions and coherence effects.

Abstract

We discuss the implementation of physically meaningful branching ratios between the CRD and PRD contributions to the emissivity of a polarized multi-term atom in the presence of both inelastic and elastic collisions. Our derivation is based on a recent theoretical formulation of partially coherent scattering, and it relies on a heuristic diagrammatic analysis of the various radiative and collisional processes to determine the proper form of the branching ratios. The expression we obtain for the emissivity is $\varepsilon=\left[\varepsilon^{\tiny (1)}-\varepsilon^{\tiny (2)}_{\rm f.s.} \right]+\varepsilon^{\tiny (2)}$, where $\varepsilon^{\tiny (1)}$ and $\varepsilon^{\tiny (2)}$ are the emissivity terms for the redistributed and partially coherent radiation, respectively, and where "f.s." implies that the corresponding term must be evaluated assuming a flat-spectrum average of the incident radiation.