We present a theory of the transition from a low-density electron crystal to a uniform electron gas based on the density-functional formalism. We find a first-order transition near $r_s=26\mathrm{}$; for $r_s$ slightly greater than the transition value the electrons must still be regarded as itinerant, but with inhomogeneous density. As a step in our calculation we find a new value for the low-density limit of the exchange-correlation energy to replace Wigner's well-known form.

• Received 10 April 1978

DOI:https://doi.org/10.1103/PhysRevB.18.6506