Perturbation theory and the radial distribution function of the square-well fluid

Perturbation theory is used to derive the first-order term of the inverse temperature expansion of the radial distribution function (RDF) for a fluid whose molecules have a hard core. Exact and approximate expressions, based on the local compressibility approximation, the superposition approximation (SA), and the Percus-Yevick theory (PY) are derived. Numerical results are examined in the case of the square-well potential with wellwidth 0.50. The RDF resulting from the exact and SA expression yield good results for the equation of state down to reduced temperatures below βε=1.