Properties of the square-well fluid of variable width

The free energy of a classical system of particles interacting with a square-well potential is calculated as a function of the width of the well. An expansion around a reference system of definite range is made, and the range difference is treated as a small parameter. The short-range case is obtained when a hardsphere system is used as reference. This expansion is carried out to third order in the width of the well, and leads to closed-form expressions which are analytic in the range and the thermodynamic variables, except for two quadratures. These can be resolved by the use of the superposition approximation or the Percus-Yevick theory. Results are obtained for the first two terms of the free energy in a high temperature expansion and are compared with Monte Carlo data. The method gives very good results for short range and most of the fluid range.