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Separation of the Interaction Potential into Two Parts in Treating Many‐Body Systems. I. General Theory and Applications to Simple Fluids with Short‐Range and Long‐Range Forces
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4.A major obstacle has been the difficulty in obtaining the solutions of these equations in a tractable enough form to be sure just what they predict about liquids, especially in transition and critical regions. Furthermore even where these equations have been solved numerically it is difficult to assess their worth because of uncertainty of the exact form of intermolecular potentials of real systems and lack of molecular dynamical or Monte Carlo results comparable in accuracy to corresponding hard‐sphere results.
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12.An ordering of graphs suitable for long‐range potentials was used in a somewhat ad hoc fashion in the work of Ref. 10. Its use as a tool in a strict γ‐expansion appears to have been first used in Ref. 11. (cf. footnote 11 and 14 in that reference).
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15.M. Fisher, “The Free Energy of a Macroscopic System,” Arch. Ratl. Mech. and Analysis 17, 377 (1964). These conditions on the potential also guarantee the convergence of the fugacity and virial expansions in a finite domain, cf. Ref. 3. This gives some meaning to our graphical manipulations.
16.J. L. Lebowitz and J. K. Percus, J. Math. Phys. 4, 1495 (1963). The definitions on the various correlation functions used here as well as their representation as Variational derivatives of the grand partition function is given in Sec. II of this reference.
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20.Hemmer’s (Ref. 13) expression for A through does not contain the term This term makes no contribution to the pressure, cf. (6.16).
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