Estimating the radiative part of QED effects in systems with supercritical charge

The effective interaction of the electron magnetic moment anomaly with the Coulomb field of superheavy nuclei is investigated by taking into account its dynamical screening at small distances. The shift of the electronic levels, caused by this interaction, is considered for H-like atoms and for compact nuclear quasi-molecules, non-perturbatively both in $Z\alpha$ and (partially) in $\alpha/\pi$. It is shown that the levels shift reveals a non-monotonic behavior in the region $Z\alpha>1$ and near the threshold of the lower continuum decreases both with the increasing the charge and with enlarging the size of the system of Coulomb sources. The last result is generalized to the total self-energy contribution to the levels shift and so to the possible behavior of radiative QED effects with virtual photon exchange near the lower continuum in the supercritical region.