Hypernetted-chain Euler-Lagrange equations and the electron fluid

Least upper bounds to the ground-state energy of the electron fluid are obtained by solving Euler-Lagrange equations obtained within the framework of Fermi hypernetted-chain theory for arbitrary density and spin polarization. It is shown that the so-obtained approximate distribution and structure functions satisfy known exact relations in the high- and low-density limits as well as in the long-wavelength limit at any density. The numerical results are in excellent agreement with coupled-cluster perturbational and Monte Carlo type calculations. As a by-product a simple analytic solution accurate in the high-density limit is obtained which is superior to the randomphase approximation in the metallic density regime.