| Abstract
| - We calculate the generic van der Waals parameters A and B for a square well model by means of a perturbationtheory. To calculate the pair distribution function or the cavity function necessary for the calculation of Aand B, we have used the Percus−Yevick integral equation, which is put into an equivalent form by means ofthe Wiener−Hopf method. This latter method produces a pair of integral equations, which are solved by aperturbation method treating the Mayer function or the well width or the functions in the square well regionexterior to the hard core as the perturbation. In the end, the Mayer function times the well width is identifiedas the perturbation parameter in the present method. In this sense, the present perturbation method is distinctfrom the existing thermodynamic perturbation theory, which expands the Helmholtz free energy in a perturbationseries with the inverse temperature treated as an expansion parameter. The generic van der Waals parametersare explicitly calculated in analytic form as functions of reduced temperature and density. The van der Waalsparameters are recovered from them in the limits of vanishing density and high temperature. The equation ofstate thus obtained is tested against Monte Carlo simulation results and found reliable, provided that thetemperature is in the supercritical regime. By scaling the packing fraction with a temperature-dependent hardcore, it is suggested to construct an equation of state for fluids with a temperature-dependent hard core thatmimicks a soft core repulsive force on the basis of the equation of state derived for the square well model.
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