ON THE SOLUTIONS OF THE HYPERNETTED-CHAIN EQUATION INSIDE THE GAS-LIQUID COEXISTENCE REGION

We present a detailed study of the solutions of the hypernetted chain integral equation inside the gas-liquid coexistence region for simple Lennard-Jones fluids. The study is performed by means of a hybrid Newt on-Raphson algorithm extended to cope with complex solutions. In this way, we have unequivocally confirmed that the origin of the well-known HNC singular behavior inside the coexistence curve is linked to the o nset of complex solutions. As density is increased starting from the v apor phase along isotherms inside the coexistence region, another sing ularity is encountered (very likely linked with the existence of a com plex multiple solution point), and correlations start to diverge. Ther efore, with the numerical approach here presented it is not feasible t o join the liquid and vapor phases through an analytically continuous path of real and complex solutions. Finally, a study of the transition from the mean spherical approximation behavior (characterized by the presence of a spinodal divergence) to the peculiar hypernetted chain s ort of singularity is also presented.