Perturbation theory for the radial distribution functions of dipolar and quadrupolar hard-sphere fluids

The radial distribution functions for the dipolar and the quadrupolar hard-sphere fluids are calculated by means of statistical-mechanical perturbation theory to third order using the hypernetted-chain (HNC) theory to approximate the perturbation terms. For both fluids the perturbation expansions through third order disagree with computer simulations, indicating that the expansion converges slowly. On the other hand, a Pade approximant, constructed from the second and third-order HNC terms, for each radial distribution function agrees excellently with the computer simulations.

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