Nonperturbative effects caused by the radiative component of the electron magnetic moment in hydrogen-like atoms

Abstract

The lower levels of the discrete spectrum of a hydrogen-like atom are calculated within the point-like nucleus approximation with nonperturbative consideration for the Schwinger interaction of the radiative component of the magnetic moment of a free electron with the Coulomb field of a nucleus. The behavior of the 1s1/2, 2s1/2, 2p1/2, and 2p3/2 levels is investigated depending on the nuclear charge values, including the range of Z > 137, where the Dirac Hamiltonian continues to be self adjoint in the presence of the Schwinger term. It is shown that the Schwinger interaction for large Z causes significant changes in the properties of the discrete spectrum; in particular, the first level that reaches the threshold of a negative continuum is 2p1/2 and this occurs at Z = 147. The behavior of the g-factor of an electron for the 1s1/2 and 2p1/2 states as a function of Z is considered as well and it is shown that for extremely large charges the correction to the g-factor due to the Schwinger term becomes a very significant effect.