In statistical mechanics the Percus–Yevick approximation is a closure relation to solve the Ornstein–Zernike equation. It is also referred to as the Percus–Yevick equation. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function. The approximation is named after Jerome K. Percus and George J. Yevick.
The direct correlation function represents the direct correlation between two particles in a system containing N − 2 other particles. It can be represented by
where is the radial distribution function, i.e. (with w(r) the potential of mean force) and is the radial distribution function without the direct interaction between pairs included; i.e. we write . Thus we approximate c(r) by
If we introduce the function into the approximation for c(r) one obtains
This is the essence of the Percus–Yevick approximation for if we substitute this result in the Ornstein–Zernike equation, one obtains the Percus–Yevick equation:
- Percus, Jerome K. and Yevick, George J. Analysis of Classical Statistical Mechanics by Means of Collective Coordinates. Phys. Rev. 1958, 110, 1, doi:10.1103/PhysRev.110.1
- Wertheim, M. S. Exact Solution of the Percus-Yevick Integral Equation for Hard Spheres. Phys. Rev. Lett. 1963, 10, 321-323, doi:10.1103/PhysRevLett.10.321