We show, for small values of z, that the solution of the Kirkwood‐Salsburg equation approaches, in the norm topolgy, the solution of the Kirkwood‐Monroe and van Kampen equations if the potential of interaction is the Kac potential φ (x12) =γsg(γx12) and the limit γ→0 is taken. We have to assume that the function g is bounded and absolutely integrable and that Σi≠j (γxij) ⩾−mB (B<∞), the the sum being performed over all pairs of the m particles.
REFERENCES
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For these potentials the Kirkwood‐Monroe and van Kampen equations are, as shown by Gates in Ref. 4, identical. See
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Nevertheless, it would be desirable to work along these lines, for one knows that in certain cases mean field theory may be exact in the limit See
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Recently, a somewhat different approach to the theory of freezing has been made by Raveché and Stuart.12 It strongly indicates the possibility of a density distribution function with a periodic structure occuring at the limit of the metastable liquid phase. Work connected with this question is also in progress in the frame of the γ expansions presented in this paper.
12.
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© 1976 American Institute of Physics.
1976
American Institute of Physics
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