Three-particle correlation function and structural theories of dense metallic liquids

Abstract

The first member of the Born-Green-Yvon hierarchy relates the pair correlation function g(r) and the three-particle correlation function g 3 via an (assumed) pair potential φ(r). With the further assumption that the pair potential φ(r) and the potential of mean force separately possess their own Fourier transforms, one can derive the result that S(k)∼φ(k)/k B T = -⩳(k), where S(k) is the liquid structure factor, ∼φ(k) the Fourier transform of φ(r), while ⩳(k) can be written in terms of the Fourier components of g 3 and φ(r). It is then shown that the precise form of ⩳(k) can be calculated for the one-component plasma in two dimensions with a ln r interaction for one particular coupling strength using the analytical pair function of Jancovici. This exact result is compared with results from two approximate dense liquid structural theories. Finally, some results are also presented for the liquid alkali metals Na and K near their freezing points, invoking electron theory for their pair potentials and X-ray m...