Instability and Melting of the Electron Solid

The electron solid, originally postulated by Wigner as the low-density limit of the hypothetical electron plasma, is shown to be unstable against breakdown of uniformity in the background charge distribution for $r_s>6.4\mathrm{}$, where $r_s$ is the radius of the unit sphere in Bohr radii. The effects which arise when the background charge is lumped into homogeneous ion cores of fixed size are then considered, and it is shown that the differences in the correlation energies and equilibrium densities of the alkali metals can be qualitatively explained by this model. Since the melting "criteria" which have previously been applied to the electron solid are independent of the question of stability, the two principal criteria are next critically reviewed, and it is demonstrated that an improvement of the argument of de Wette leads to a predicted melting density which corresponds to $r_s\approx 27$. The improved melting condition is applied to solid hydrogen at zero temperature and is shown to agree quite closely with an explicit thermodynamic calculation of the melting point for this case. The predicted melting density is 4.5×${10}^6$ g/cc.