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We study the ground state solutions of the Dirac-Fock model in the case ofweak electronic repulsion, using bifurcation theory. They are solutions of amin-max problem. Then we investigate a max-min problem coming from theelectron-positron field theory of Bach-Barbaroux-Helffer-Siedentop. We showthat given a radially symmetric nuclear charge, the ground state of Dirac-Focksolves this max-min problem for certain numbers of electrons. But we alsoexhibit a situation in which the max-min level does not correspond to asolution of the Dirac-Fock equations together with its associatedself-consistent projector

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