Dielectric Response Function of Electron Liquids. III: Numerical Investigation of Static Properties

Numerical investigations of the static properties of the electron liquid are carried out on the basis of the dielectric response function derived by one of the authors. The static form factor is computed over the thermodynamically stable domain of the plasma parameter, ε≲10. The correlation energy thus obtained is in good agreement with the numerical experiment carried out by Brush, Sahlin and Teller; the short-range behavior of the correlation is much improved over the existing theories. The compressibility sum rule is well satisfied up to ε≃10 so that the critical plasma parameter for the onset of a thermodynamic instability is determined to be in the range, 9.2≤εc ≤10.9. The nature of such an instability is clarified with the aid of the fluctuation analysis of the positive-charge background; a critical fluctuation of Ornstein-Zernike type is thus predicted. For the electron liquid with ε> εc, a possibility of separation into two phases is pointed out.