Born-Green equation: Difference between revisions
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The '''Born-Green equation''' is given by: | |||
:<math>k_B T \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}= | :<math>k_B T \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}= | ||
\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> | \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> | ||
Latest revision as of 18:49, 6 September 2007
The Born-Green equation is given by:
![{\displaystyle k_{B}T{\frac {\partial \ln {\rm {g}}(r_{12})}{\partial {\mathbf {r} }_{1}}}={\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d3a7d316a708e5b2aaaf57f0c335adb93f09c2d1)
where is the intermolecular pair potential, T is the temperature, and is the Boltzmann constant.
