Angular and polarization correlations in two--photon decay of hyperfine 2s states in hydrogenlike ions

TL;DR

This paper investigates the angular and polarization correlations of photon pairs emitted during two-photon decay of hyperfine 2s states in hydrogenlike ions using relativistic quantum theory, revealing distinct emission patterns for different transition types.

Contribution

It provides a detailed relativistic analysis of angular and polarization correlations in two-photon decay of hyperfine states, identifying distinct patterns for spin-flip and non-spin-flip transitions.

Findings

Non-spin-flip transitions show a $1+ ext{cos}^2 heta$ angular distribution.

Spin-flip transitions exhibit a $1-rac{1}{3} ext{cos}^2 heta$ angular distribution.

Polarizations are parallel for non-spin-flip and orthogonal for spin-flip transitions.

Abstract

The angular and polarization properties of the photon pair emitted in the two--photon decay of $2s$ hyperfine states in hydrogenlike ions are investigated within the relativistic Dirac framework and second order perturbation theory. The studied transitions are $2s_{1/2}\,(F=1,0)\to1s_{1/2}\,(F=1,0)$ in Hydrogen atom and $2s_{1/2}\,(F=4,3)\to1s_{1/2}\,(F=4,3)$ in hydrogenlike Uranium ion. Two different emission patterns are found: For non-spin-flip transitions, the angular correlation ($i.e.$ the angular distribution of the emitted photons) is of the type $\sim 1+\cos^2\theta$, while the linear polarizations of the emitted photons are approximately parallel one another; For spin-flip transitions, the angular correlation is of the type $\sim 1-1/3\cos^2\theta$, while the linear polarizations of the emitted photons are approximately orthogonal one another.