Abstract: Barker and Henderson's Compressibility approximation is improved by assuming that the numbers of molecules in neighbour spherical shells are correlated.The results are better than those of Barker and Henderson's Macroscopic Compressibility Approximation (B-H Ma.Appro.) and Local Compressibility Approximation(B-H Lo.C. Appro .) specially at high densities.Asimple and accurate analytic representation of square-well potential hard sphere perturbation theory is derived based upon this improvement.Anew form of radial distribution function is proposed and applied.The theory is tested by calculating thermodynamic properties with the four-term truncated form, and the results are in good agreement with those of Monte Carlo and Molecular Dynamics computer simulation calculations.

Key words: Compressibility approximation, Perturbation theory, Equation of state, Thermodynamic properties