14 - Two-component theory of pure liquid metals

Summary

In this chapter we shall report on developments in liquid-metal theory in which, instead of dealing with ions coupled by effective interactions mediated by the conduction electrons, the liquid metal is treated as a two-component system, conduction electrons and positive ions (Cowan and Kirkwood, 1958; Watabe and Hasegawa, 1973; Chihara, 1973; March and Tosi, 1973). Earlier, evidence has been presented for well-defined collective modes of the positive ions in liquid Rb near its melting point. There is, of course, no doubt that, in any dense assembly of conduction electrons, there are well-defined plasma modes. Therefore, a workable model to keep in mind for such a two-component system begins with the assumption that there are two types of well-defined collective excitations; density fluctuations (analogous to phonons in a crystal) and plasmons (Tosi and March, 1973a; for details see Appendix 14.1).

Following the approach of March and Tosi (1973), the two-component theory will be developed in terms of three partial structure factors, S_ii = S, the nuclear-nuclear structure factor as observed by neutron scattering, the electron-electron structure factor S_ee, and the “cross” correlations represented by S_ie(k).

Electron-ion Hamiltonian and density fluctuation operators

To implement the programme just outlined, let us set up a description of the liquid metal in terms of the local number densities ρ_e(r, t) and ρ_i(r, t) of electrons and ions, respectively, at position r and time t.