6 Interacting electron gas
We now turn to describing the properties of interacting electrons in metals. To a first approximation, we regard the ions as providing only a uniform background of positive charge to compensate the overall charge of the electrons. Such an approximation constitutes the Jellium model, first introduced by Herring and characterized extensively by Pines (P1955). For ions of charge Z and density ni, the electron density ne equals Zni. We start by considering the Hartree–Fock approximation to the uniform interacting electron system, which applies at high densities, and later introduce further approximations to treat the dilute regime of the interacting electron gas.
Typically, we associate the eigenstates