Analytical expressions for the radial free space distribution function of the hard-sphere system and the phase transition

The radial free space distribution function (RFSDF) has been defined and calculated for the hard-sphere fluid and solid. Fittings for the RFSDF of the hard-sphere fluid and solid are presented and analytical expressions for RFSDF are also presented. From the analysis of RFSDFs, the solid and fluid phase are clearly distinguished.