  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. The location of this
boundary is not fixed, but it can be chosen to lie at arbitrarily high values
of wavevector and energy, well clear from the Fermi level of jellium. We
conclude that, rather than the lack of screening in the HF equations, the
well-known qualitative failure of the ground-state HF approximation is an
artifact of its nonlocal exchange operator. Other similar artifacts of the HF
nonlocal exchange operator, not associated with the lack of electronic
correlation, are known in the literature.
