Application of complementary variational principles to the Kirkwood equation for hard spheres at very high densities

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Abstract
The theory of complementary variational principles for a nonlinear integral equation with symmetric positive‐definite kernel is applied to the Kirkwood equation (under the superposition approximation) for g(2)(x) for a system of hard spheres at very high densities. At all λ values beyond the lower bound on the limit of stability of the dense fluid regime, variational analysis of the approximate analytical g(2)(x) functions suggests infinite periodicity in g(2)(x). This behavior is in agreement with an earlier study of high density solutions to the Kirkwood equation for hard spheres, where the solutions were obtained by iterative techniques.

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