QED in Strong Coulomb Fields: Charged Vacuum, Atomic Clock, and Correlated, Narrow e+e−-Lines

Abstract

When atomic structure is extrapolated from the known boundary of chemical elements (nuclear charge Z=109) into the region Z=170−190, one finds that the 1s 1/2-state, the atomic K-shell, gains tremendously in binding energy. As shown in Fig. 1 the 1s 1/2-state — and also the next higher state, the 2p 1/2-level — traverses the gap between the positive and negative energy continuum solutions of the Dirac equation, and is predicted to reach a binding energy of 2me=1.022 MeV at the critical nuclear charge Ze=173±1. The uncertainty derives from our lack of precise knowledge of the extrapolated nuclear charge distribution and from possible radiative corrections of higher order that are not accounted for in the calculations (for a point-like nuclear charge distribution the Dirac Hamiltonian is not self-adjoint for Z > α −1 ≈ 137. The origin of this is the singular behaviour of the vacuum in the point nucleus limit for Zα >1).