# Radial Distribution Function for Hard Spheres

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In statistical mechanics, the distribution of interparticle separations determines the radial distribution function [1].

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Contributed by: Andrés Santos (May 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The exact solution of the Percus–Yevick integral equation for hard spheres was first obtained in [2] and [3]. The entirely analytic forms for the static structure factor were first presented in [4].

References

[1] Wikipedia. "Radial Distribution Function." (Mar 8, 2013) en.wikipedia.org/wiki/Radial_distribution_function.

[2] M. S. Wertheim, "Exact Solution of the Percus–Yevick Integral Equation for Hard Spheres," *Physical Review Letters*, 10(8), 1963 pp. 321–323. doi:10.1103/PhysRevLett.10.321.

[3] E. Thiele, "Equation of State for Hard Spheres," *The Journal of Chemical Physics*, 39(2), 1963 pp. 474–479. doi:10.1063/1.1734272.

[4] N. W. Ashcroft and J. Lekner, "Structure and Resistivity of Liquid Metals," *Physical Review*, 145(1), 1966 pp. 83–90.

[5] Wikipedia. "Structure factor." (May 9, 2013) en.wikipedia.org/wiki/Structure_factor.

[6] Wikipedia. "Ornstein–Zernike equation." (April 20, 2013) en.wikipedia.org/wiki/Ornstein% E2 %80 %93 Zernike_equation.

[7] SklogWiki. "Bridge function." (November 7, 2012) www.sklogwiki.org/SklogWiki/index.php/Bridge_function.

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