Singularities of solution of the Ornstein-Zernike equation within a gas-liquid transition region

Gas-liquid transition regions for Lennard-Jones systems was studied with th e use of the Ornstein-Zernike equation under various conditions of its clos ure. It was shown that, for all closures, there is a turning point in the g as-phase branch of the solution near the lines of phase equilibrium that se parate physically meaningful and unfeasible solutions to the Ornstein-Zerni ke equation. A possible relation of points of singularity with lines of pha se equilibria (a binodal) and with the mechanical stability of the system ( spinodal) was discussed.