Some connections between Dirac-Fock and Electron-Positron Hartree-Fock

Jean-Marie Barbaroux, Maria J. Esteban, Eric Séré

Published 2004-02-21, updated 2004-09-02Version 3

We study the ground state solutions of the Dirac-Fock model in the case of weak electronic repulsion, using bifurcation theory. They are solutions of a min-max problem. Then we investigate a max-min problem coming from the electron-positron field theory of Bach-Barbaroux-Helffer-Siedentop. We show that given a radially symmetric nuclear charge, the ground state of Dirac-Fock solves this max-min problem for certain numbers of electrons. But we also exhibit a situation in which the max-min level does not correspond to a solution of the Dirac-Fock equations together with its associated self-consistent projector.