  We present an analytic theory of the spin-resolved pair distribution
functions $g_{\sigma\sigma'}(r)$ 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 Weizs\"{a}cker-Herring ideal kinetic energy
functional to derive a zero-energy scattering Schr\"{o}dinger equation for
$\sqrt{g_{\sigma\sigma'}(r)}$. 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 $g_{\sigma\sigma'}(r)$ 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.
