Angular and polarization analysis for two-photon decay of 2s hyperfine states of hydrogenlike Uranium

TL;DR

This paper analyzes the angular and polarization characteristics of two-photon decay in hydrogenlike uranium, highlighting relativistic effects and differences between spin-flip and non-spin-flip transitions, with implications for nuclear influence on photon emission.

Contribution

It provides a relativistic analysis of two-photon decay in hydrogenlike uranium, emphasizing polarization and angular distributions, including non-dipole and relativistic effects, for the first time.

Findings

Non-spin-flip transitions follow a $1+ ext{cos}^2 heta$ angular distribution with parallel polarizations.

Spin-flip transitions follow a $1-rac{1}{3} ext{cos}^2 heta$ distribution with orthogonal polarizations.

Deviations from dipole approximation are evaluated for both transition types.

Abstract

The amplitude of two-photon transitions between hyperfine states in hydrogenlike ions is derived based on relativistic Dirac equation and second order perturbation theory. We study angular and linear polarization properties of the photon pair emitted in the decay of $2s$ states, where spin-flip and non-spin-flip transitions are highlighted. We pay particular attention to hydrogenlike uranium, since it is an ideal candidate for investigating relativistic and high-multipole effects, such as spin-flip transitions. Two types of emission patterns are identified: i) non-spin-flip transitions are found to be characterized by an angular distribution of the type $W(\theta)\sim1+\cos^2\theta$ while the polarizations of the emitted photons are parallel; ii) spin-flip transitions have somewhat smaller decay rates and are found to be characterized by an angular distribution of the type $W(\theta)\sim1-1/3\cos^2\theta$ while the polarizations of the emitted photons are orthogonal, where $\theta$ is the angle between photons directions. Deviations due to non-dipole and relativistic contributions are evaluated for both types of transitions. This work is the first step toward exploring the effect of nucleus over the the angular and polarization properties of the photon pairs emitted by two-photon transitions.