Perturbativity vs non-perturbativity in QED-effects for H-like atoms   with $Z\alpha >1$
  The behavior of levels near the threshold of the lower continuum in superheavy H-like atoms with $Z\alpha >1$, caused by the interaction $\Delta U_{AMM}$ of the electron's magnetic anomaly (AMM) dynamically screened at small distances $ \ll 1/m$, with the Coulomb field of atomic nucleus is considered by taking into account the complete dependence of electron's wavefunction (WF) on $Z\alpha$. It is shown that the calculation of the contribution caused by $\Delta U_{AMM}$ via both the quark structure and the whole nucleus, considered as a uniformly charged extended Coulomb source, leads to results, which coincide within the accepted precision of calculations. It is shown also that there appears some difference in results between perturbative and non-perturbative methods of accounting for the contribution from $\Delta U_{AMM}$ within the corresponding Dirac equation (DE) in favor of the latter. Moreover, the growth rate of the contribution from $\Delta U_{AMM}$ reaches its maximum at $ Z \sim 140-150$, while by further increase of $Z$ into the supercritical region $Z\gg Z_{cr,1}$ the shift of levels caused by $\Delta U_{AMM}$ near the lower continuum decreases monotonically to zero. The last result is generalized to the whole self-energy contribution to the shift of levels and so to the possible behavior of radiative QED-effects with virtual photon exchange near the lower continuum. 
A. A. Roenko, K. A. Sveshnikov
physics.atom-ph