Pseudoclassical approach to electron and ion density correlations in simple liquid metals

Abstract

Electron-electron and electron-ion structural correlations in simple liquid metals are treated by using effective pair potentials to incorporate quantal effects into a pseudoclassical description of the electron fluid. An effective pair potential between simultaneous electron density fluctuations is first constructed from known properties of the degenerate jellium model, which are the plasmon sum rule, the Kimball-Niklasson relation and Yasuhara’s values of the electron pair distribution function at contact. An analytic expression is theraby obtained in the Debye-Huckel approximation for the electronic structure factor in jellium over a range of density appropriate to metals, with results which compare favourably with those of fully quantal evaluations. A simple pseudoclassical model is then set up for a liquid metal: this involves a model of charged hard spheres for the ion-ion potential and an empty-core model for the electron-ion potential, the Coulombic tails being scaled as required by the relation between the long-wave-length partial structure factors and the isothermal compressibility of the metal. The model is solved analytically by a pseudoclassical linear response treatment of the electron-ion coupling and numerical results are reported for partial structure factors in liquid sodium and liquid beryllium. Contact is made for the latter system with data on the electron-electron structure factor in the crystal from inelastic X-ray scattering experiments of Eisenberger Marra and Brown.