Dynamical screening of AMM and QED effects for H-like atoms with large Z

The effective interaction ΔU_AMM of the electron anomalous magnetic moment (AMM) with the Coulomb field of extended nucleus is considered by taking into account the dependence of the electronic form factor F₂(q²) on q² from the very beginning, which leads to dynamical screening of AMM at small distances r ≪ 1/m. Within the nonperturbative approach, the behavior of the lowest states in the field of a superheavy extended nucleus with Zα > 1, caused by ΔU_AMM, is considered. It is shown that the growth rate of the contribution from ΔU_AMM demonstrates significantly nonmonotonic behavior with increasing Z. At the same time, in the region Z ≫ Z_cr,1s the shift of the electronic levels near the threshold of the lower continuum decreases monotonically. 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 outside the perturbation theory (PT) in Zα.