Ladder approximation for three- and four-particle correlation functions: Application to thermodynamic perturbation theory

We apply the recently developed ladder approximation for three- and four-particle correlation functions to thermodynamic perturbation theory. We calculate the first correction in the perturbative expansion of the pair correlation function and the second correction in the expansion of the free energy of a fluid of particles interacting via a hard-sphere reference potential plus a perturbing term. Both calculated quantities depend on the three- and four-particle correlation functions of the reference system. The results for the free energy are in good overall agreement with computer-simulation data over a wide range of densities, up to the hard-sphere fluid-solid phase transition. The results for the pair correlation function are in good agreement with computer-simulation data except near contact at high densities.