Hartree-Fock states in the thermodynamic limit. II. Generalized Overhauser orbitals

Two infinite families of two-parameter generalized Overhauser orbitals are introduced and shown to satisfy explicitly, for occupied states, the self-consistent Hartree-Fock equations in the thermodynamic limit. For an attractive $\delta$ interaction, they give lower Hartree-Fock energy than the usual plane-wave solutions, even for relatively weak coupling and/or low density. The limiting members (possessing an infinite number of harmonics) of both families appear to tend to a "classical static lattice" state, via a second-order transition for one family and via first order for the other. The related density profiles and energy expressions are calculated as functions of the two new parameters. A direct variation with respect to these parameters was done numerically and results are presented graphically.