Two-Photon Emission of a Hydrogenlike Atom with Photon Polarization and Electron Spin States Taken into Account

The process of two-photon emission (Ze)* → (Ze) + 2γ of a hydrogenlike atom is considered with spin states of the electron and polarization of the photons taken into account, which had not been done before. A general expression for the probability of the process per unit time has been obtained for different polarization states of the photons with a formulation of hard and soft selection rules for the quantum numbers m and l. It is shown that by virtue of the established specifics of the properties of the two-photon emission process (absence of a Zeeman effect and dependence of the probability on the polarization states of the photons), it can in principle be identified against the background of single-photon emission (Ze)* → (Ze) + γ, despite the presence of additional small factors: 1) α = e2/ћc ≈ 1/137 of the perturbation theory in e, and 2) the square of the atomic expansion parameter (Zα)2 in the expression for the probability.