m-state Interference with Partial Frequency Redistribution for Polarized Line Formation in Arbitrary Magnetic Fields

Abstract

The present paper concerns the derivation of polarized partial frequency redistribution (PRD) matrices for scattering on a two-level atom in arbitrary magnetic fields. We generalize the classical theory of PRD that is applicable to a J = 0 → 1 → 0 scattering transition, to other types of atomic transitions with arbitrary quantum numbers. We take into account quantum interference between magnetic substates of a given upper J-state. The generalization proceeds in a phenomenological way, based on the direct analogy between the Kramers-Heisenberg scattering amplitude in quantum mechanics and the Jones scattering matrix in classical physics. The redistribution matrices derived from such a generalization of classical PRD theory are identical to those obtained from a summed perturbative quantum electrodynamic treatment of the atom-radiation interaction. Our semi-classical approach has the advantage that it is non-perturbative, more intuitive, and lends itself more easily to further generalization (like the inclusion of J-state interference in the PRD theory).