A semi empirical compact equation of state for hard sphere fluids at any density

We propose a new semi empirical expression of the equation of state for a hard sphere fluid which is valid in the disordered phases over the whole density range below and above the freezing point. Starting from the existing numerical results for the virial coefficients, we elaborate a compact expression for the equation of state which is compatible both with the low and medium density behaviour (disordered stable phase) and with the asymptotic high density behaviour (disordered metastable phase). The resulting equation of state has a compact form and exhibits a simple pole at the close random packing density and a double pole at a density equal to 1. That equation of state only depends on the following quantities: the virial coefficients B2, B3 ,B4, which can be exactly computed, the random packing density ξ0, which is imposed by statistical geometry, and the residue of the pole in ξ0. The results are in a fairly good agreement with the numerical data.