Ladder approximation for three- and four-particle correlation functions

An example of an application of a recently developed generalized Ornstein-Zernike formalism to the numerical evaluation of equilibrium three- and four-particle correlation functions is given. Using a simple closure approximation leading to the ladder approximation we have numerically evaluated dipole-dipole-interaction correlation functions for a polarizable nonpolar hard-sphere fluid. These functions depend on the three- and four-particle correlation functions and describe a correction to the Clausius-Mossoti formula for the dielectric constant and an integrated intensity measured in depolarized light scattering experiments. Qualitative agreement with computer simulation data was found for a wide range of densities up to the fluid-solid phase transition. For high densities the ladder approximation yeilds much better results than the Kirkwood superposition approximation, which becomes useless in this context at liquid-state densities.