Kirkwood superposition approximation

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Kirkwood 1935 (Eq. 40 Ref. 1, Eq. 5.6 Ref. 2)


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)


It appears that this was used as a basis of a closure for the Kirkwood 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 and the compressibility equation if this superposition approximation is used to generate g(r).

References

  1. [JCP_1935_03_00300]
  2. [PRSA_1946_188_0010]
  3. Tohru Morita and Kazuo Hiroike "A New Approach to the Theory of Classical Fluids. I" Progress of Theoretical Physics 23 pp. 1003-1027 (1960)
  4. [PR_1952_085_000777]
  5. [PRSA_1953_216_0203]