A criterion for determining the coupling and the exponent [K(η,β) and ζ(η,β)] of the one-Yukawa generalized mean spherical approximation (GMSA), which better describes a given real fluid, is suggested. The relative spatial configuration of the surface (≡${\Sigma }_{\chi }$) where the compressibility diverges, with respect to the surface (≡${\Sigma }_{\Delta }$) bounding the region where physical solutions of the GMSA equations exist, is studied in terms of K, ζ, and η (the packing fraction). ${\Sigma }_{\chi }$ is found to lie always in the physically accessible region and to become tangent to ${\Sigma }_{\Delta }$ along the η axis; that consequently will be the locus of the critical points of the real systems. By the aforesaid criterion we show that the Baxter solution of the adhesive hard-sphere model can be obtained from the limit of the GMSA solution as ζ→∞. The study of the limit ζ→0 shows that the GMSA critical indices are generally different from the mean-field ones and that their values depend on the way ζ approaches zero as one moves along the critical isochore and the critical isotherm. Attention is also called to the fact that, as ζ→0, K(η,ζ)/${\zeta }^2$ has a minimum at η=0.128, a value rather close to the critical densities of the real fluids.

• Received 21 March 1988

DOI:https://doi.org/10.1103/PhysRevA.38.4121