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| The '''Born-Green equation''' is given by:
| | <math>kT \frac{\partial \ln g(r_{12})}{\partial r_1}= |
| | \frac{-\partial U(r_{12})}{\partial r_1}- \rho \int \left[ \frac{\partial U(r_{13})}{\partial r_1} \right] g(r_{13})g(r_{23}) ~ d r_3</math> |
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| :<math>k_B T \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}=
| | ==References== |
| \frac{-\partial \Phi(r_{12})}{\partial {\mathbf r}_1}- \rho \int \left[ \frac{\partial \Phi(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23}) ~ {\rm d}{\mathbf r}_3</math>
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| where <math>\Phi(r_{nm})</math> is the [[intermolecular pair potential]], ''T'' is the [[temperature]], and <math>k_B</math> is the [[Boltzmann constant]].
| | #M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, volume 188 p. 10" (1946) |
| ==References==
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| #[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)] | |
| [[category:statistical mechanics]]
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