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The low-density electron gas in the spin-extended Hartree-Fock approximation

The spin-extended Hartree-Fock approximation with localized overlapping orbitals is applied to the low-density electron gas problem. A procedure is outlined which in the case of small overlap makes the energy per electron convergent when the number of electrons tends to infinity. As a first approximation the perfect pairing case is considered. It is shown that the singlet ground state energy lies in between the energies of ferromagnetic and antiferromagnetic states for any perfect pairing structure in second order in the overlap approximation.