Editing Kirkwood superposition approximation
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[[John G. Kirkwood]] (Eq. 40 Ref. 1, Eq. 5.6 Ref. 2) | |||
:<math> | :<math>g_N^{(3)}(r_1,r_2,r_3)=g_N^{(2)}(r_1,r_2)g_N^{(2)}(r_2,r_3)g_N^{(2)}(r_3,r_1)</math> | ||
It appears that this was used as a basis of a closure for the | It appears that this was used as a basis of a closure for the | ||
Kirkwood | Kirkwood integral equation (Ref. 1) and the Yvon, and Born-Green | ||
(Ref. 2) until the work of Morita and Hiroike (Ref. 3). | (Ref. 2) until the work of Morita and Hiroike (Ref. 3). | ||
It was pointed out in Ref.s 4 and 5, that there is an inconsistency between | It was pointed out in Ref.s 4 and 5, that there is an inconsistency between | ||
the | the pressure and the compressibility equation if this superposition approximation is used to generate <math>g(r)</math>. | ||
This approximation is rigorously correct for one-dimensional systems, and is only true in three-dimensions in the limit of zero density. | This approximation is rigorously correct for one-dimensional systems, and is only true in three-dimensions in the limit of zero density. | ||
==References== | ==References== | ||
#[http://dx.doi.org/10.1063/1.1749657 John G. Kirkwood, "Statistical Mechanics of Fluid Mixtures", Journal of Chemical Physics '''3''' pp. 300-313 (1935)] | #[http://dx.doi.org/10.1063/1.1749657 John G. Kirkwood, "Statistical Mechanics of Fluid Mixtures", Journal of Chemical Physics '''3''' pp. 300-313 (1935)] | ||
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#[http://dx.doi.org/10.1103/PhysRev.85.777 B. R. A. Nijboer and L. Van Hove "Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation", Physical Review '''85''' pp. 777 - 783 (1952)] | #[http://dx.doi.org/10.1103/PhysRev.85.777 B. R. A. Nijboer and L. Van Hove "Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation", Physical Review '''85''' pp. 777 - 783 (1952)] | ||
#[http://links.jstor.org/sici?sici=0080-4630%2819530122%29216%3A1125%3C203%3AOTTOF%3E2.0.CO%3B2-5 G. S. Rushbrooke and H. I. Scoins "On the Theory of Fluids", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, '''216''' pp. 203-218 (1953)] | #[http://links.jstor.org/sici?sici=0080-4630%2819530122%29216%3A1125%3C203%3AOTTOF%3E2.0.CO%3B2-5 G. S. Rushbrooke and H. I. Scoins "On the Theory of Fluids", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, '''216''' pp. 203-218 (1953)] | ||
# | #[http://dx.doi.org/10.1143/PTP.21.421 Ryuzo Abe "On the Kirkwood Superposition Approximation", Progress of Theoretical Physics '''21''' pp. 421-430 (1959)] | ||
[[Category: Statistical mechanics]] | [[Category: Statistical mechanics]] |