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
2s1/2(F=1,0)→1s1/2(F=1,0) in Hydrogen atom and
2s1/2(F=4,3)→1s1/2(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
∼1+cos2θ, while the linear polarizations of the emitted photons are approximately parallel one another; For spin-flip transitions, the angular correlation is of the type
∼1−1/3cos2θ, while the linear polarizations of the emitted photons are approximately orthogonal one another.
The amplitude of two-photon transitions between hyperfine states in hydrogenlike ions is derived based on the 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 $W(\ensuremath{\theta})\ensuremath{\sim}1+{cos}^{2}\ensuremath{\theta}$ while the polarizations of the emitted photons are parallel; and (ii) spin-flip transitions have somewhat smaller decay rates and are found to be characterized by an angular distribution of the type $W(\ensuremath{\theta})\ensuremath{\sim}1\ensuremath{-}1/3{cos}^{2}\ensuremath{\theta}$ while the polarizations of the emitted photons are orthogonal, where $\ensuremath{\theta}$ is the angle between photons directions. Deviations due to nondipole and relativistic contributions are evaluated for both types of transitions. This work is the first step toward exploring the effect of the nucleus over the angular and polarization properties of the photon pairs emitted by two-photon transitions.
Two-photon decay of hydrogenlike ions is studied within the framework of second-order perturbation theory, based on the relativistic Dirac's equation. Special attention is paid to the effects arising from the summation over the negative-energy (intermediate virtual) states that occur in such a framework. In order to investigate the role of these states, detailed calculations have been carried out for the $2{s}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}$ and $2{p}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}$ transitions in neutral hydrogen H as well as for hydrogenlike xenon
Xe53+ and uranium
U91+ ions. We found that for a correct evaluation of the total and energy-differential decay rates, summation over the negative-energy part of Dirac's spectrum should be properly taken into account both for high-
Z and low-
Z atomic systems.