Editing Pair distribution function
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For a fluid of <math>N</math> particles, enclosed in a volume <math>V</math> at a given | For a fluid of <math>N</math> particles, enclosed in a volume <math>V</math> at a given temperature <math>T</math> | ||
([[canonical ensemble]]) interacting via the `central' [[intermolecular pair potential]] <math>\Phi(r)</math>, the two particle distribution function is defined as | ([[canonical ensemble]]) interacting via the `central' [[intermolecular pair potential]] <math>\Phi(r)</math>, the two particle distribution function is defined as | ||
:<math>{\rm g}_N^{(2)}( | :<math>{\rm g}_N^{(2)}(r_1,r_2)= V^2 \frac | ||
{\int ... \int e^{-\beta \Phi(r_1,...,r_N)}{\rm d}r_3...{\rm d}r_N} | |||
{\int e^{-\beta \Phi(r_1,...,r_N){\rm d}r_1...{\rm d}r_N}}</math> | |||
where <math>\beta | where <math>\beta = 1/(k_BT)</math>, where <math>k_B</math> is the [[Boltzmann constant]]. | ||
==Exact convolution equation for <math> | ==Exact convolution equation for <math>g(r)</math>== | ||
See Eq. 5.10 of Ref. 1: | See Eq. 5.10 of Ref. 1: | ||
:<math>\ln | :<math>\ln g(r_{12}) + \frac{\Phi(r_{12})}{kT} - E(r_{12}) = n \int \left(g(r_{13}) -1 - \ln g(r_{13}) - \frac{\Phi(r_{13})}{kT} - E(r_{13}) \right)(g(r_{23}) -1) ~{\rm d}r_3</math> | ||
==See also== | ==See also== | ||
*[[Radial distribution function]] | *[[Radial distribution function]] | ||
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==References== | ==References== | ||
#[http://dx.doi.org/10.1088/0034-4885/28/1/306 J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics '''28''' pp. 169-199 (1965)] | #[http://dx.doi.org/10.1088/0034-4885/28/1/306 J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics '''28''' pp. 169-199 (1965)] | ||
[[category: statistical mechanics]] | [[category: statistical mechanics]] |