On the Schwartz-Ehrenreich closure relations for correlation functions in simple fluids

The closure relation for a correlation function of third order suggested by Schwartz and Ehrenreich in the framework of the electron theory of liquid metals is substituted into the formal relation connecting g(2) with g(3). The equation determining the radial distribution function, obtained in this way, is solved for the fluid of hard spheres. Comparison of this solution with the solution of the Born-Green-Yvon equation and with the exact results for a hard-sphere fluid indicates that the closure relation due to Schwartz and Ehrenreich is inferior to the superposition approximation due to Kirkwood.