An extension of the Overhauser model for nuclear matter

Abstract

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.