Generalized mean spherical approximation for hard spheres

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Abstract
The mean spherical approximation for molecules with a hard core has been solved [1], for the case where the direct correlation function is, outside the core, of the form of a Yukawa function. Despite recent simplifications, this solution is implicit and rather complex and, as a result, there are few numerical results. If the parameters, K and z, of this Yukawa tail are adjusted to give the known pressure and compressibility of a fluid of hard spheres, this solution can be used to obtain a generalized mean spherical approximation (GMSA) for the direct correlation function and the radial distribution function (RDF) of the hard-sphere fluid. Numerical results for K, z, and the RDF of the hard-sphere fluid are obtained. The GMSA RDF is found to be in excellent agreement with the simulation values. In addition, it is observed that for this system at high densities (the region of greatest interest) z is large and K is small. This fact is used to obtain a simple and explicit approximation to the full solution. This approximate solution is also found to be in close agreement with the machine simulation results for hard spheres.