  Model of hard sphere system is important part of modern theories of liquids.
Radial distribution function of hard sphere fluid represented in form of
explicit analytical expression allows to obtain thermodynamic potentials in
analytical form, which is very helpful for further analysis and applications. A
new analytical expression of radial distribution function of hard sphere fluid
is developed. The density derivative of the radial distribution function and
the first two terms of Barker-Henderson perturbation theory are derived as
analytical expressions. The obtained results agree well with published
simulation data. These results have important implications for real fluid
modeling using density functional theory and perturbation theories.
