On the optimized cluster theory for continuous potentials

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Abstract
The optimized cluster theory (OCT) of Andersen and Chandler is reexamined in the light of the recent generalization of the mean spherical approximation (MSA) to continuous potentials. The diagrammatic structure of the ’’renormalized potential’’ arises naturally from this version of the MSA and is found to contain diagrams with f0 bonds between root points. These f0 bonds preclude the topological reduction carried out by Andersen et al. A modification of the renormalized potential is introduced which permits the topological reduction to be performed. The implications concerning the convergence of the OCT are discussed in light of these modifications. It is also shown that the OCT provides an a priori rationale for preferring a perturbative form of the hypernetted-chain approximation to the corresponding form of the Percus–Yevick approximation.