Unified description of metallic and neutral liquids and plasmas

Abstract

A formulation to evaluate equilibrium properties of a non-simple metallic liquid and plasma is presented in a unified fashion involving a neutral liquid as a special case; a multi-centre problem is to be solved in a coupled manner with a single-centre problem in this formulation. A liquid metal or a plasma is taken as a binary mixture of nuclei and electrons. Firstly, an inhomogeneous nucleus-electron mixture caused by fixing a nucleus at the origin is investigated by the density-functional theory for a single-centre problem to determine the internal electronic structure of an ion at the origin, which enables the authors to think of a liquid metal as an ion-electron mixture composed of ions with the same electronic structure as the central ion so built up at the origin. Thus, the radial distribution functions, a self-consistent potential for electrons and the ionic charge are obtained, if the bare ion-ion interaction is given beforehand; these quantities are used to solve the following multi-centre problem. Secondly, the problem of treating a homogeneous nucleus-electron mixture is reduced to the multicentre problem of an inhomogeneous electron gas under the external potential caused by randomly distributed nuclei. Thus, this system is shown to be regarded as a classical one-component fluid described by an effective Hamiltonian, with the same interparticle potential as the effective interionic interaction obtained in the previous single-centre problem; a bare ion-ion interaction is now created by an extension of the Gordon-Kim (GK) or tight-binding bond (TBB) model. This formulation offers a generalization of the GK and TBB methods to take account of the presence of the conduction electrons with use of self-consistent bound-state functions in a liquid. Here, a bound state is defined as a state with a negative eigenvalue or a resonant state with a long lifetime. The internal energy of a liquid metal is expressed in terms of output from the single-centre problem based on the nucleus-electron model.