On triplet potentials in the theory of classical fluids

The possibility of introducing triplet potentials into a theory of fluids at the level of the first order HNC and P.Y. theories is discussed. If we do so we obtain extended theories which, at low densities, give the third virial coefficient correctly. More generally, we are led to an effective pair potential which is a linear function of the density of the fluid. Reference is made to the relevant experimental work of Mikolaj and Pings.