Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

A method for calculating the electronic levels in the compact superheavy nuclear quasi-molecules, based on solving the two-center Dirac equation using the multipole expansion of two-center potential, is developed. For the internuclear distances up to $d\sim100$~fm such technique reveals a quite fast convergence and allows for computing the electronic levels in such systems with accuracy $\sim 10^{-6} $. The critical distances $R_{cr}$ between the nuclei for $1\sigma_g$ and $1\sigma_u$ electronic levels in the region $Z\simeq 87-100$ are calculated. By means of the same technique the shifts of electronic levels due to the effective interaction $\Delta U_{AMM}$ of the electron's magnetic anomaly with the Coulomb field of the closely spaced heavy nuclei are evaluated as a function of the internuclear distance and the charge of the nuclei, non-perturbatively both in $Z\alpha$ and (partially) in $\alpha/\pi$. It is shown, that the levels shifts near the lower continuum decrease with the enlarging size of the system of Coulomb sources both in the absolute units and in units of $Z^4 \alpha^5 / \pi n^3$. The last result is generalized to the whole self-energy contribution to the level shifts and so to the possible behavior of radiative part of QED-effects with virtual photon exchange near the lower continuum in the overcritical region.