ANALYSIS OF THE HYPERNETTED-CHAIN EQUATION FOR IONIC FLUIDS

It is well known that the numerical solution of the hypernetted chain (HNC) equations yields satisfactory results for the pair correlation f unction of the primitive model of electrolytes and similar models of i onic particles over a considerable range of thermodynamic states. Desp ite this, it has become apparent that for low densities (or low ionic concentration in electrolytes) the numerical solution breaks down for temperatures well above the expected coexistence region between gas an d liquid phases. Here we study the situation by analytic means, compar ing it to a similar problem for sticky hard spheres in the Percus-Yevi ck (PY) approximation. On the basis of our analysis we conclude that t he failure of the HNC is of the same nature and is connected to the ex istence of two possible solutions for low densities. When the temperat ure is lowered these solutions will merge into one at a particular tem perature, below which a real solution is no longer possible. By extend ing our analysis to systems like the monoatomic Lennard-Jones fluid an d comparing with previous results of Gallerani, Lo Vecchio and Reatto for two-Yukawa and Lennard-Jones systems in the PY approximation, we c onclude that these are general common features of the HNC and PY appro ximations in the low-density regime. Numerically they appear to persis t in the HNC closure at high densities as well (in contrast to the beh aviour of the PY approximation) although our analysis is silent in thi s regard. Our analysis is consistent with the results of a recent comp rehensive numerical study by Belloni.