A correction for the Hartree-Fock density of states for jellium without screening.

We revisit the Hartree-Fock (HF) calculation for the uniform electron gas, or jellium model, whose predictions--divergent derivative of the energy dispersion relation and vanishing density of states (DOS) at the Fermi level--are in qualitative disagreement with experimental evidence for simple metals. Currently, this qualitative failure is attributed to the lack of screening in the HF equations. Employing Slater's hyper-Hartree-Fock (HHF) equations, derived variationally, to study the ground state and the excited states of jellium, we find that the divergent derivative of the energy dispersion relation and the zero in the DOS are still present, but shifted from the Fermi wavevector and energy of jellium to the boundary between the set of variationally optimised and unoptimised HHF orbitals.