Photon-polarization effects and their angular dependence in relativistic two-photon bound-bound transitions

The quantum-electrodynamic theory of photon-polarization effects in two-photon bound-bound atomic transitions is developed, including relativistic and retardation effects. The differential cross section for photon scattering from a randomly oriented target is expressed in terms of eight polarization correlation parameters a_i which are associated with vector products involving the photon polarizations. We restrict our detailed discussions to the case of photon scattering from atoms, though the results are easily generalized to other situations. Symmetry arguments are used to establish the necessary conditions for these polarization effects to occur. One of the eight parameters a_i describes circular dichroism in the case that the scattered photon has a suitable linear polarization, and another describes the appearance of elliptically polarized scattered photons for the case of a suitable linearly polarized incident beam. The particular cases of atomic scattering with J_i = J_f = 0 and 1/2 (where J_i and J_f are the total angular momenta of the initial and final states of the target, respectively) are analysed in detail. Numerical estimates of the parameters are given for ground-state atoms in the J_i = J_f = 0 approach, using the independent-particle approximation, and for 1s_1/2→1s_1/2 and 2p_3/2 transitions in hydrogen-like ions, demonstrating the feasibility of experimental observation of the above-mentioned circular dichroic effect in high-Z atoms and ions.