A semi empirical expression of the virial coefficients for hard sphere fluids at all density

We propose a new semi empirical expression of the virial coefficients for a hard sphere fluid which is valid in the disordered phase over the whole density range. The results are in good agreement with the numerical data and better than those of the well-known Carnahan & Starling equation of state in the domain of validity of the later; moreover this new expression accounts for the singularity which is required for the equation of state at the close random packing limit.