Dielectric formulation of strongly coupled electron liquids at metallic densities. IV. Static properties in the low-density domain and the Wigner crystallization

Thermodynamic and correlational properties of strongly coupled degenerate electron liquids are investigated in the low-density domain down to $r_s=70\mathrm{}$, on the basis of the dielectric formulation developed in previous papers. Comparing the liquid ground-state energy with various evaluations of the crystalline energy, we estimate $r_s=12-27\mathrm{}$ as the transition density at which the Wigner crystallization may take place. The possibility of other instabilities is also noted.