Quantum theory of pure liquid metals as two-component systems

Abstract

With the ultimate aims of clarifying the interpretation and the utility of effective ion-ion interactions in liquid metals, and of understanding the unusual isotopic mass dependence of the shear viscosity of liquid metal Li, a fully quantum statistical mechanical theory is developed from the many-body Hamiltonian of the conduction electron-positive ion assembly. We have set up quantum equations of motion which are analogs of classical continuity and conservation equations by expanding the equation for the Wigner distribution function about its diagonal. The most important of these equations for our present purposes relates the time derivative of the current density j(r, t) to the flux of current and to density-density correlation functions for electrons, electron-ions, and ions. This theory is then applied to neutron scattering by liquid metals. While the theory is sufficiently general in principle to treat electron-ion interaction of arbitrary strength, it is shown that when the interacion is weak, the usual results are recovered, along with the effective ion-ion interaction. In this latter connection, it is also demonstrated how the effective Ornstein-Zernike function C( q) in a liquid metal is related to bare ion and bare electron direct correlation functions and to the bare electron partial structure factor. Combining C( q) with one of the classical equations of liquid structure such as Born-Green or Percus-Yevick then relates the effective ion-ion interaction to the partial correlation functions of the bare ions and electrons. It is further shown how gradient expansions of the correlation functions lead to equations of motion for the density, current, and energy density which are simply the hydrodynamic equations of the present quantum theory of two-component systems. It is pointed out that the analog of the Navier-Stokes equation for the two-component system may be used to identify the quantity 4 3 η + ζ for the liquid metal, η and ζ being respectively the shear and bulk viscosities. Finally, it is demonstrated that 4 3 η + ζ depends explicitly on functional derivatives of the nonequilibrium pair distribution functions of ion-ion, electron-ion, and electron-electron correlations.