Hartree-Fock Ground State Research Articles

Stability of the Plane Wave Hartree-Fock Ground State

The condition that the plane wave state is the lowest Hartree-Fock state of a large fermion system with repulsive interactions, is generally investigated and applied to the systems with $\ensuremath{\delta}$-type interactions, finite-range interactions, and long-range Coulomb interactions. It is found that for finite-range interactions the plane wave state is stable in both the high-density and low-density regions, but may become unstable in the intermediate-density region. The high-density stable region disappears for $\ensuremath{\delta}$-type interactions, while the low-density stable region vanishes for long-range Coulomb interactions. Especially for an electron gas, the critical value ${r}_{s}$ is smaller than 4.5. A speculation concerning the transition of the true ground state is discussed.

An extension of the Overhauser model for nuclear matter

Overhauser has recently proposed a single-particle trial wave function for the ground state of a system of Fermi particles with attractive two-body point interactions. We have re-investigated this problem for the case of finite range attractive and repulsive two-body forces. It is shown that the magnitude of the energy gap above the ground state is diminished or disappears completely; the spatial density variations for both spin directions are smaller than for a point interaction. The two density functions oscillate in-phase when the two-body potential is attractive and in-phase opposition for repulsive forces. For certain potentials we are able to construct a Hartree-Fock ground state which has a lower energy than that obtained with simple Overhauser wave functions. This ground state has a region in momentum space, inside the Fermi sea, which is not occupied by any particles. However, for reasonable strengths and ranges of the two-body force the Overhauser ground state is the lowest one obtained and an energy gap occurs.