An alternative formulation of the virial expansion for simple fluids
A new analytical formulation of the virial expansion for simple fluids is presented. Starting from the usual expression of the partition function of a set of identical molecules, a Fourier transformation is performed. Then a systematic procedure formally allowing the computation of the virial coefficients in the reciprocal space is presented; the coefficients are finally expressed as multiple integral expressions in the reciprocal space, and focus is on the simple case of hard sphere fluids. Finally, an approximate recursion relation is proposed that allows an estimation to be obtained of those coefficients without having to actually perform the integrations; a comparison of the results is made with the equation of state by Carnahan and Starling and with the recent numerical results by Clisby and Mc Coy.