High Z effects in accounting for radiative component of the electron magnetic moment in hydrogen-like atoms

The behavior of electron energy levels in hydrogen-like atoms is studied while taking into account the nonperturbative interaction between the radiative component of the magnetic moment of a free electron Δg_free and the Coulomb field of an atomic nucleus with charge Z, including those with Z > 137. It is shown that for Zα ≪ 1 the energy-level shift is rather effectively determined through the matrix elements of the corresponding Dirac-Pauli operator with relativistic Coulomb wave functions. At the same time, for superheavy nuclei with Z ∼ 170, this shift, generated by Δg_free, is genuinely nonperturbative, behaves like ∼Z⁵ near the threshold of negative continuum, exceeds all the estimates of radiative corrections coming from vacuum polarization and electron self-energy known so far, and turns out to be at least of the same order as the effects of nuclear charge screening by filled electron shells.