Abstract
The Kirkwood integral equations for triplet or higher-order correlation functions are examined with a view to obtain some useful approximate sets of integral equations for correlation functions. Based on a set where the potential energies are eliminated from the integral equations for triplet or higher-order correlation functions, the Percus-Yevick integral equation is obtained. The derivation is rather simple but requires a pair of assumptions. This derivation implies that the Percus-Yevick equation is essentially founded on the Kirkwood superposition approximation which is one of the assumptions. A couple of plausible extensions of the Percus-Yevick equation are then suggested for pair correlation function and their consequences are examined in the light of some exact relations for pair correlation function. One of such generalized equations is numerically solved to assess its accuracy.
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