Relativistic polarization analysis of Rayleigh scattering by atomic hydrogen

TL;DR

This paper presents a relativistic analysis of Rayleigh scattering polarization properties in atomic hydrogen using the Dirac equation, exploring angular distributions and polarization degrees across various photon energies and scattering angles.

Contribution

It introduces a relativistic framework for polarization analysis in Rayleigh scattering, including analytical expressions applicable to hydrogenic and multi-electron systems, with detailed computations for energies 0.5 to 10 keV.

Findings

Higher-order nondipole effects significantly influence polarization.

Analytical formulas accurately describe angular distributions.

Results applicable to both hydrogen and complex atomic systems.

Abstract

A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second order perturbation theory. The relativistic atomic states used for the calculations are obtained by making use of the finite basis set method and expressed in terms of $B$ splines and $B$ polynomials. We introduce two experimental scenarios in which the light is circularly and linearly polarized, respectively. For each of these scenarios, the polarization-dependent angular distribution and the degrees of circular and linear polarization of the scattered light are investigated as a function of scattering angle and photon energy. Analytical expressions are derived for the polarization-dependent angular distribution which can be used for scattering by both hydrogenic as well as many-electron systems. Detailed computations are performed for Rayleigh scattering by atomic hydrogen within the incident photon energy range 0.5 to 10 keV. Particular attention is paid to the effects that arise from higher (nondipole) terms in the expansion of the electron-photon interaction.