  A new analytical approach to derive an approximate equation of state and the
virial coefficients for simple fluids is presented. Starting from the usual
expression of the partition function, we first perform a Fourier
transformation, and then we implement an original approximation scheme of the
correlation terms in the reciprocal space. A procedure involving combinatorial
analysis and partial re-summations leads to simple expressions for the virial
coefficients, which are effectively calculated for hard sphere fluids. A
comparison is made with Carnahan & Starling equation of state and with the
available numerical results for the virial coefficients. The virial
coefficients calculated within our approximation scheme are in rather good
agreement with the known computed values up to order 6, i.e. at low density; if
we extrapolate those results for higher orders we obtain a simple equation of
state in good agreement with the experimental data for the stable fluid phase.
