Density expansion of the radial distribution and bridge functions of the hard sphere fluid

The bridge function and the background correlation function ( and consequently the radial distribution function) of the pure hard sphere fluid are expanded up to the sixth power in density. The calculations are based on the Ree-Hoover representation of the diagrams and Monte Carlo integration. The coefficients as functions of the particle-particle separation are fitted to splines taking into account discontinuities in higher derivatives up to the term of the order of (r - const)(5).