Editing Kirkwood superposition approximation

The '''Kirkwood superposition approximation''' takes its name from [[John G. Kirkwood]]  (see Eq. 40 Ref. 1, Eq. 5.6 Ref. 2)


:<math>{\rm g}_N^{(3)}({\mathbf r}_1,{\mathbf r}_2,{\mathbf r}_3)={\rm g}_N^{(2)}({\mathbf r}_1,{\mathbf r}_2){\rm g}_N^{(2)}({\mathbf r}_2,{\mathbf r}_3){\rm g}_N^{(2)}({\mathbf r}_3,{\mathbf r}_1)</math>


It appears that this was used as a basis of a closure for the
Kirkwood [[integral equations |integral equation]] (Ref. 1) and the Yvon, and Born-Green
(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
the [[Pressure equation |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. 
==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://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and  H. S. 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)]
#[http://dx.doi.org/10.1143/PTP.23.1003 Tohru Morita and Kazuo Hiroike "A New Approach to the Theory of Classical Fluids. I" Progress of Theoretical Physics '''23''' pp. 1003-1027 (1960)]
#[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://dx.doi.org/10.1143/PTP.21.421 Ryuzo Abe "On the Kirkwood Superposition Approximation", Progress of Theoretical Physics '''21''' pp. 421-430 (1959)]
#[http://dx.doi.org/10.1063/1.1725757     Russell V. Cochran and L. H. Lund "On the Kirkwood Superposition Approximation", Journal of Chemical Physics '''41''' pp.  3499-3504 (1964)]
#[http://dx.doi.org/10.1088/0034-4885/31/2/301 G. H. A. Cole "Classical fluids and the superposition approximation", Reports on Progress in Physics '''31''' pp. 419-470 (1968)]
[[Category: Statistical mechanics]]