Radial distribution function of a hard-sphere fluid

A hard-sphere fluid (8788 particles) is modeled by the Monte Carlo method for 41 occupation coefficients in the range of eta = 0.10-0.50 (step 0.01). The radial distribution functions were determined at 512 points in an interval of up to five hard sphere radii. In this interval, the number of analyzed particle pairs was from 1.8.10(9) to 9.0.10(9) (eta = 0.10-0.50). The two-variable function g(r,eta) was analytically expressed using least-squares analysis; standard deviation from the Monte Carlo data was of the or-der of 0.001. An equation of state is suggested for a hard-sphere fluid (standard deviation 0.002). A direct comparison shows that at high densities the accuracy of the expressions is one order of magnitude higher than that of the best relations reported in the literature.