# Editing Kirkwood superposition approximation

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β | + | [[John G. Kirkwood]] (Eq. 40 Ref. 1, Eq. 5.6 Ref. 2) | |

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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 | ||

β | 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 | ||

β | 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. | ||

It has recently been shown that the Kirkwood superposition approximation precludes the existence of a critical point (Ref. 6). | It has recently been shown that the Kirkwood superposition approximation precludes the existence of a critical point (Ref. 6). |