The free energy and the equation of state of a hard-sphere system for homogeneous stable and metastable phases

A new free energy equation is deduced; it serves as a basis for the derivation of an equation for the homogeneous phase of a hard-sphere system. It exactly reproduces all the known virial coefficients and agrees with the molecular dynamics data within their accuracy. The absence of singular points during transition from the stable region to the metastable region is shown. According to the properties of the statistical integral, the free energy and the equation of state have a singularity at close packing.