# Percus Yevick

If one defines a class of diagrams by the linear combination (Eq. 5.18 Ref.1) (See G. Stell in Ref. 2)

one has the exact integral equation

The Percus-Yevick integral equation sets *D(r)=0*.
Percus-Yevick (PY) proposed in 1958 Ref. 3

The Percus-Yevick closure relation can be written as (Ref. 3 Eq. 61)

or

or (Eq. 10 in Ref. 4)

or (Eq. 2 of Ref. 5)

where is the intermolecular pair potential.

In terms of the bridge function

Note: the restriction arising from the logarithmic term Ref. 6.
A critical look at the PY was undertaken by Zhou and Stell in Ref. 7.

## See also[edit]

## References[edit]

- J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics
**28**pp. 169-199 (1965) - G. Stell "PERCUS-YEVICK EQUATION FOR RADIAL DISTRIBUTION FUNCTION OF A FLUID", Physica
**29**pp. 517- (1963) - Jerome K. Percus and George J. Yevick "Analysis of Classical Statistical Mechanics by Means of Collective Coordinates", Physical Review
**110**pp. 1 - 13 (1958) - G. A. Martynov and G. N. Sarkisov "Exact equations and the theory of liquids. V", Molecular Physics
**49**pp. 1495-1504 (1983) - Forrest J. Rogers and David A. Young "New, thermodynamically consistent, integral equation for simple fluids", Physical Review A
**30**pp. 999 - 1007 (1984) - Niharendu Choudhury and Swapan K. Ghosh "Integral equation theory of Lennard-Jones fluids: A modified Verlet bridge function approach", Journal of Chemical Physics,
**116**pp. 8517-8522 (2002) - Yaoqi Zhou and George Stell "The hard-sphere fluid: New exact results with applications", Journal of Statistical Physics
**52**1389-1412 (1988)