Generalized mean spherical approximations of the dense hard-sphere fluid

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Abstract
After having discussed how integral equations of the Percus-Yevick type can be generated stemming from known approximations of the direct correlation function (DCF), we show that in the case of the hard-sphere (HS) fluid they can be recast into the generalized mean spherical approximation form by using truncated Dirichlet’s series. The analysis is numerically carried through by using present knowledge of second- and third-order approximations of the DCF. The virial and compressibility pressures tend to close on the Carnahan-Starling values, but improvement in the radial distribution functions is noteworthy only in the contact region, while the Waisman thermodynamical consistent approximation appears to be the most accurate one. The mechanical stability of the system is analyzed: For all the considered approximations the HS system appears mechanically stable.