Jean-Marie BARBAROUX, Maria J. ESTEBAN, Eric SERE
Some connections between Dirac-Fock and Electron-Positron
Hartree-Fock
(400K, Postscript)
ABSTRACT. 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.