Stability of the relativistic electron-positron field of atoms in Hartree-Fock approximation: Heavy elements

Abstract

We show that the modulus of the Coulomb Dirac operator with a sufficiently small coupling constant bounds the modulus of the free Dirac operator from above up to a multiplicative constant depending on the product of the nuclear charge and the electronic charge. This bound sharpens a result of Bach et al citeBachetal1999 and allows to prove the positivity of the relativistic electron-positron field of an atom in Hartree-Fock approximation for all elements occurring in nature.