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We present an analytic theory of the spin-resolved pair distributionfunctions $g_{\sigma\sigma'}(r)$ and the ground-state energy of an electron gaswith an arbitrary degree of spin polarization. We first use the Hohenberg-Kohnvariational principle and the von Weizs\"{a}cker-Herring ideal kinetic energyfunctional to derive a zero-energy scattering Schr\"{o}dinger equation for$\sqrt{g_{\sigma\sigma'}(r)}$. The solution of this equation is implementedwithin a Fermi-hypernetted-chain approximation which embodies the Hartree-Focklimit and is shown to satisfy an important set of sum rules. We presentnumerical results for the ground-state energy at selected values of the spinpolarization and for $g_{\sigma\sigma'}(r)$ in both a paramagnetic and a fullyspin-polarized electron gas, in comparison with the available data from QuantumMonte Carlo studies over a wide range of electron density.Comment: 13 pages, 8 figures, submitted to Phys. Rev.

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