Iterative method for the study of the thermodynamic behavior of hard-sphere Yukawa fluids

Semi-analytic expressions for the calculation of the thermodynamic properties of the hard-sphere Yukawa fluid are derived from the solution of the Ornstein–Zernike equation according to the mean spherical approximation. These expressions are written in terms of a cumulative parameter Γ that becomes the physically meaningful root of a fourth (or larger) order polynomial, which can be determined directly by a proposed iterative method. The method is illustrated by comparison against well known results including predictions from perturbation theories, and its limitations are discussed.