Analytic theory of ground-state properties of a three-dimensional electron gas with arbitrary spin polarization

We present an analytic theory of the spin-resolved pair distribution functions $g_{\sigma {\sigma }^{\prime }}\mathrm{}\left(r\right)\mathrm{}$ and the ground-state energy of an electron gas with an arbitrary degree of spin polarization. We first use the Hohenberg-Kohn variational principle and the von Weizsäcker-Herring ideal kinetic-energy functional to derive a zero-energy scattering Schrödinger equation for $\sqrt{g_{\sigma {\sigma }^{\prime }}\mathrm{}\left(r\right)\mathrm{}}.$ The solution of this equation is implemented within a Fermi-hypernetted-chain approximation which embodies the Hartree-Fock limit and is shown to satisfy an important set of sum rules. We present numerical results for the ground-state energy at selected values of the spin polarization and for $g_{\sigma {\sigma }^{\prime }}\mathrm{}\left(r\right)\mathrm{}$ in both a paramagnetic and a fully spin-polarized electron gas, in comparison with the available data from quantum Monte Carlo studies over a wide range of electron density.