Abstract: A simple and accurate analytic representation of square-well potential hard sphere perturbation theory is derived based upon the Zwanzig perturbation method. The higher-order perturbation terms are obtained by using the Barker-Henderson approximation. A new form of radial distribution function g(R)=1/ηgj(η/(1-η))~j is proposed and applied. The theory is tested by calculating thermodynamic properies with the four-term truncated form of the (η/(1-η)) expansions and compared with available Monte Carlo and Molecular Dynamics computer simulation calculations. The results are in good agreement.