A max - min principle for the ground state of theDirac - Fock functional

In this paper, we prove that, when the ne structure constant is small enough, the energy of the \ground state" of the Dirac-Fock model can be obtained by a nonlinear max-min principle. 1. The Dirac-Fock model. In 6] we proved that solutions of Dirac-Fock equations converge, in a certain sense, towards solutions of the Hartree-Fock equations when the speed of light tends to innnity. This limiting process allowed us to deene a notion of ground state for the Dirac-Fock equations, valid when the ne structure constant is small enough. In the present paper we show, as a consequence of our results in 6], that the energy of this ground state can be deened as a max-min level. We hope that this new characterization will Membre de l'Institut universitaire de France. Partially supported by the A.C.I. blanche \Mod eles math ematiques pour la chimie quantique atomique et mol eculaire".