Quantum Statistical Theory of Electron Correlation

The average electrostatic potential distribution about a given electron is calculated for a system of point-charge electrons embedded in a neutralizing continuum of positive charge. The calculation is classical, involving a Poisson equation of the Debye-Hückel type, except that the electron density is treated by means of Fermi-Dirac statistics as in the Thomas-Fermi theory of the atom. The calculated energy due to electrostatic interactions agrees with the quantum-mechanical exchange plus correlation energy over the observed range of metal valence-electron densities, $2\leqq r_s\leqq 6$, but is too small at larger and smaller densities. ($r_s$ is the electron-sphere radius in units of the Bohr radius.) The equilibrium density ($T=p=0\mathrm{}$) occurs at $r_s=4.3\mathrm{}$, at which point the compressibility is 69 per megabar. The electronic specific heat is linear in $T$ at low temperatures and varies from 0.9 to 0.74 of the Sommerfeld value over the observed metal density range.