Percus Yevick

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If one defines a class of diagrams by the linear combination (Eq. 5.18 Ref.1) (See G. Stell \cite{P_1963_29_0517_nolotengoElsevier})

one has the exact integral equation

The Percus-Yevick integral equation sets D(r)=0. Percus-Yevick (PY) proposed in 1958 \cite{PR_1958_110_000001}

The {\bf PY} closure can be written as (\cite{PR_1958_110_000001} Eq. 61)

or

or (Eq. 10 \cite{MP_1983_49_1495})

or (Eq. 2 of \cite{PRA_1984_30_000999})

or in terms of the bridge function


Note: the restriction $-1 < \gamma (r) \leq 1$ arising from the logarithmic term \cite{JCP_2002_116_08517}. The HNC and PY are from the age of {\it `complete ignorance'} (Martynov Ch. 6) with respect to bridge functionals. A critical look at the PY was undertaken by Zhou and Stell in \cite{JSP_1988_52_1389_nolotengoSpringer}.

References

  1. [RPP_1965_28_0169]