Polarization correlations in the two--photon decay of hydrogen--like ions

Polarization properties of the photons emitted in the two-photon decay of hydrogen-like ions are studied within the framework of the density matrix and second-order perturbation theory. In particular, we derive the polarization correlation function that gives the probability of the (two-photon) coincidence measurement performed by polarization-sensitive detectors. Detailed calculations of this function are performed for the $2s_{1\mathrm{/}2}\to 1s_{1\mathrm{/}2}$ transition in neutral hydrogen as well as Xe${}^{53+}$ and U${}^{91+}$ ions. The obtained results allow us to understand the influence of relativistic and non-dipole effects on the polarization correlations in the bound-bound two-photon transitions in heavy ions.