  In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is
unstable to a spin density wave (SDW) instability. Determining the true HF
ground state has remained a challenge. Using numerical calculations for finite
systems and analytic techniques, we study the HF ground state of the 3D
electron gas. At high density, we find broken spin symmetry states with a
nearly constant charge density. Unlike previously discussed spin wave states,
the observed wave vector of the SDW is smaller than $2 k_F$. The
broken-symmetry state originates from pairing instabilities at the Fermi
surface, a model for which is proposed.
