Three-dimensional electron gas with localization along one, two, and three directions

A powerful non-perturbative technique, which allows a direct evaluation of the ground state properties of an interacting electron gas in three dimensions, has been developed. In a unified approach, the low-, intermediate-, and high-density regions are considered. This technique is applied to three-dimensional (3D) systems with periodic electron density along one and two directions. The electronic and magnetic states of these systems are theoretically studied on the basis of the deformable jellium model, within a self-consistent Hartree–Fock approach. To determine the magnetic character of the 3D electron gas ground state, the paramagnetic and ferromagnetic energies are calculated and compared at low, intermediate, and high densities. As rs increases, several symmetry and/or magnetic transitions occur, in each system. The electronic and magnetic states obtained are compared with other theoretical results reported in the literature with different models. In addition to planar and linear periodic electron densities, cubic electron densities are considered in order to look for symmetry transitions among these systems.