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

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 $\sim 1+\cos^2θ$, while the linear polarizations of the emitted photons are approximately parallel one another; For spin-flip transitions, the angular correlation is of the type $\sim 1-1/3\cos^2θ$, while the linear polarizations of the emitted photons are approximately orthogonal one another.