Hartree-Fock test of Overhauser's model with a Skyrme force

The Overhauser problem in nuclear matter is re-examined carefully with a modern density dependent Skyrme interaction. The energy per particle, at each density, is obtained as a function of three 'order parameters' (which vanish for the spatially homogeneous plane-wave cas) and which are momentum integrals over the k-dependent Overhauser orbital mixture coefficients, which in turn are determined by the three original 'order parameters'. Spurious energy minima are eliminated by self-consistently solving the above non-linear problem numerically. The Overhauser Hartree-Fock state is more stable than the plane-wave state only in a density region safely below the nuclear saturation density value. This fact is interpreted as embryonic of alpha-cluster formation at sub-nuclear densities. (Auth.)