Spatial correlations in the electron gas: Path integral Monte Carlo simulation

Abstract

Thermally excited states of the three-dimensional electron gas in a neutralizing background are computed by path integral Monte Carlo simulation for values of the Wigner-Seitz radius within the interval 5 < r s < 15. Coulomb and exchange interactions, permutation symmetry, and spin state are treated explicitly. Variation of electron correlation functions with density and temperature is analyzed. Quantum effects suppress and enhance spatial correlation at low and high densities, respectively. Transition between the electron-gas states characterized by these opposite trends corresponds to a density of approximately 2.5 × 1021 cm−3. A transition line between liquid-like and gaslike phases is determined in the temperature-density diagram. Weak anisotropy of many-body correlations in the liquid-like state stimulates excitation of spherically symmetric collective rotational modes. The effective short-range pseudopotential exhibits strong temperature dependence due to exchange effects. For strongly correlated systems, the characteristic screening length deviates from that predicted by the Thomas-Fermi screening model ( $$ \sim \sqrt {r_s } $$ ), approaching a linear function of r s. The effective short-range interaction substantially differs from the Yukawa potential in mean field theory. Coulomb interaction shifts the Fermi level up by an order of magnitude or higher, and this effect becomes stronger with decreasing density.