Perturbative and nonperturbative aspects of the interaction of Dirac particle's AMM with the Coulomb field of a superheavy nucleus

Within perturbative and significantly nonperturbative approaches, the behavior of the lowest levels of the Dirac particle due to the interaction ΔU_AMM of the particle's anomalous magnetic moment (AMM) with the Coulomb field of nucleus with Zα > 1 is considered by taking into account the complete dependence of particle's wavefunction (WF) on Zα. The contribution from ΔU_AMM was calculated via both the nucleus considered as a uniformly charged extended Coulomb source and as a distributed system of point u- and d-quarks. It is shown that in both cases nonperturbative account of ΔU_AMM in the Dirac equation (DE) leads to coinciding results. At the same time, specificity of ΔU_AMM is manifested in the fact that for Δg ≃ const the results of perturbation theory (PT) and nonperturbative calculations differ significantly, whereas in the case of dynamical screening of AMM at short distances the perturbative and nonperturbative methods of accounting ΔU_AMM in DE are practically the same.