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On integral equations for the pair correlation function

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  • Eu, Byung Chan
  • Gan, Hin Hark

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.

Suggested Citation

  • Eu, Byung Chan & Gan, Hin Hark, 1991. "On integral equations for the pair correlation function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(2), pages 265-284.
    • Handle: RePEc:eee:phsmap:v:171:y:1991:i:2:p:265-284
    DOI: 10.1016/0378-4371(91)90278-K
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    1. McCarthy, W.O. & Hodgson, N. & Briggs, J.E., 1966. "Dairy Farm Amalgamation and Increased Farm Output," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 34(01), pages 1-7, March.
    2. Jean Poirier, 1968. "Les fonctions sociales de l'ostentation économique," Revue Tiers Monde, Programme National Persée, vol. 9(33), pages 3-16.
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