For a fluid of
particles, enclosed in a volume
at a given temperature
(canonical ensemble) interacting via the `central' intermolecular pair potential
, the two particle distribution function is defined as
![{\displaystyle {\rm {g}}_{N}^{(2)}({\mathbf {r} }_{1},{\mathbf {r} }_{2})=V^{2}{\frac {\int ...\int e^{-\beta \Phi ({\mathbf {r} }_{1},...,{\mathbf {r} }_{N})}{\rm {d}}{\mathbf {r} }_{3}...{\rm {d}}{\mathbf {r} }_{N}}{\int e^{-\beta \Phi ({\mathbf {r} }_{1},...,{\mathbf {r} }_{N})}{\rm {d}}{\mathbf {r} }_{1}...{\rm {d}}{\mathbf {r} }_{N}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/450354cc005edaa0aa2e735687a7aa0c1683d410)
where
, where
is the Boltzmann constant.
Exact convolution equation for ![{\displaystyle g(r)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e09e9ec780782afb0b2ae8c172811dba1e4eb63c)
See Eq. 5.10 of Ref. 1:
![{\displaystyle \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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/12416d343dd52dd99d6e087441707b5bfdf44a43)
where
.
See also
References
- J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics 28 pp. 169-199 (1965)