Energy, Specific Heat, and Magnetic Properties of the Low-Density Electron Gas

A perturbation expansion in powers of {rₒ}^-1{2} has been used to investigate the ground-state energy of a dilute electron gas, the result being, in rydberg units per particle, E=-1. 792{rₒ}+2. 66{{rₒ}^3{2}}+b{{rₒ}^2}+O (1{{rₒ}^5{2}}) +terms falling off exponentially with {rₒ}^1{2}. The dimensionless parameter rₒ is the radius of the unit sphere in Bohr radii. The term in {rₒ}^-1 is the energy of a body-centered cubic lattice of electrons as calculated by Fuchs; the {rₒ}^-3{2} term is the zero-point vibrational energy of the lattice, as obtained from a calculation of the normal modes, the result differing only by a small amount from the values estimated by Wigner; and b{rₒ}^-2 is the first-order effect of anharmonicities in the vibration. The constant b has been estimated, its magnitude being smaller than unity. The vibrational part of the specific heat has been calculated, and a first-order approximation has been obtained for the exponential terms in the energy. Part of this energy comes from exchange, which leads to the result that, except for very low densities (rₒ270), the electron spins are antiferromagnetically aligned. An order of magnitude for the N\'eel temperature has been calculated.