SINGULARITIES IN THE CONSISTENT HYPERNETTED-CHAIN APPROXIMATION

We use the consistent set of hypernetted chain (HNC) equations to inve stigate the stability of liquid and vapor phases of simple fluids. We calculate the phase diagram and discuss the physical (spinodal) and ma thematical (termination line) singularities of the theory. The latter delimits a region where the HNC equations have no physically acceptabl e solutions. Additionally, we confirm that the physical solutions of t he HNC equation correspond to local minima of the consistent grand pot ential which, however, appears to be unbounded from below.