Two-photon decay of inner-shell vacancies in heavy atoms

Based on the second-order perturbation theory, we investigate the two-photon decay of K-shell vacancies in heavy atoms. The many-electron transition amplitude that occurs in the theory is evaluated by means of the independent particle approximation (IPA). By using this approach, computations are performed for the decay of neutral gold and are directly compared with recent experimental data, not relying on any scaling assumptions. The obtained results confirm previously identified discrepancies between the IPA theory and the experiment for the 2s -> 1s transition, and an apparent "resonance" region of the 3s -> 1s transition, but they show a moderate agreement with the measured data for the 3d -> 1s and 4s + 4d -> 1s cases. Moreover, with the help of the IPA we discuss the validity of the nonrelativistic scaling that was employed in the past to estimate the relative two-photon transition probabilities P in heavy atoms based on calculations done for lighter elements and different decay geometries. We find, in particular, that the electric-dipole angular distribution of emitted photons holds rather well even in the high-Z domain, while the assumption that the relative probability P is independent of nuclear charge may result in 10-30% inaccuracy of theoretical predictions.