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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 Zα and (partially) in α/π. It is shown that the levels shift reveals a non-monotonic behavior in the region Zα>1 and near the threshold of thedoi:10.1051/epjconf/201920109010 fatcat:u6gotlpshrbopcjsgluo7sonb4