A unifying polarization formalism for electric- and magnetic-multipole interactions

TL;DR

This paper develops a comprehensive tensor formalism for describing electric and magnetic multipole interactions with polarized radiation, enabling advanced modeling of atomic scattering and magnetic field effects.

Contribution

It introduces a unified spherical tensor formalism for multipole interactions, extending polarization treatment to all multipole orders using spherical-wave expansion.

Findings

Modeling of radiation anisotropy in electric-quadrupole transitions

Application to Hanle effect in magnetic fields

Unified tensor framework for electric and magnetic multipoles

Abstract

We extend the spherical tensorial formalism for polarization to the treatment of electric- and magnetic-multipole transitions of any order. We rely on the spherical-wave expansion to derive the tensor form of the operator describing the interaction of the atomic system with a polarized radiation field, which naturally leads to the introduction of spherical tensors describing the polarization properties of the interacting field. As a direct application, the formalism is used to model the radiation anisotropy affecting the scattering of radiation in an electric-quadrupole transition, and the associated Hanle effect in the presence of a magnetic field.