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Journal of Statistical Physics

, Volume 61, Issue 5–6, pp 1187–1201 | Cite as

Moments of the Percus-Yevick hard-sphere correlation function

  • N. E. Berger
  • V. Twersky
Articles
  • 54 Downloads

Abstract

A simple recursive relation is derived for the momentsM n ,n=1, 2,..., of the Percus-Yevick correlation functionh(r) for identical hard spheres. TheMn are rational functions of the volume fractionw occupied by the spheres; the first ten are given explicitly, and a single-term asymptotic form is obtained to suffice for the rest. Applications of theMn(w) include testing different approximations forh by numerical integration ofh(r) r n . We compare exact moments with shell approximationsM n [h s ] corresponding to integration fromr=0 tos+1 fors=3−8, and with hybrid approximationsM n [h s +h a ] which supplement the shell approximations with integrals of an asymptotic tail froms+1 to ∞. For a givens, the hybrid approximation is better forw increasing than the shell approximation, andM n [h3+h a ] is even better thanM n [h8]

Key words

Percus-Yevick correlation function moments shell expansions asymptotic forms residue series hybrid approximations 

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • N. E. Berger
    • 1
  • V. Twersky
    • 1
  1. 1.Mathematics DepartmentUniversity of IllinoisChicago

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