3-PARTICLE CORRELATION-FUNCTION AND STRUCTURAL THEORIES OF DENSE METALLIC LIQUIDS

The first member of the Born-Green-Yvon hierarchy relates the pair cor relation function g(r) and the three-particle correlation function 93 via an (assumed) pair potential phi(r). With the further assumption th at the pair potential phi(r) and the potential of mean force separatel y possess their own Fourier transforms, one can derive the result that S(k)phi(k)/k(B)T = -E(k), where S(k) is the liquid structure factor, phi(k) the Fourier transform of phi(r), while E(k) can be written in t erms of the Fourier components Of g3 and phi(r). It is then shown that the precise form of E(k) can be calculated for the one-component plas ma in two dimensions with a In r interaction for one particular coupli ng strength using the analytical pair function of Jancovici. This exac t result is compared with results from two approximate dense liquid st ructural theories. Finally, some results are also presented for the li quid alkali metals Na and K near their freezing points, invoking elect ron theory for their pair potentials and X-ray measurements of their s tructure factors.