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# System prepended metadata

title: Percus-Yevick Theory

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# Percus-Yevick Theory

Percus-Yevick(PY) theory is a theory that discribes the states of fluid, which is consisited from **hard sphere molecules**. Percus-Yevick equation is derived by applying Percus-Yevick approximation as a **closure formula on Ornstein-Zernike equation**.


## Theory



The PY equation for hard sphere is
\begin{eqnarray}
	\tau(\vec r) = 1 + \int_{|\vec r|<R}^{}d\vec{r'}\tau(\vec{r'}) + \int_{|\vec r|>R}^{}d\vec{r'}\tau(\vec{r'})
\end{eqnarray}


## Solutions 

## Refernece
[J. K. Percus and G. J. Yevick, Phys. Rev. 110, 1 (1958)](https://journals.aps.org/pr/pdf/10.1103/PhysRev.110.1)
* Before equation(66) is about derivation of PY equation, and after (66) is refering to hard sphere systems using virial expansions.

[M. S. Wertheim, Phys. Rev. Lett. 10, 321 (1963)](https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.10.321)
 * Propose a solution to PY equations.

