Abstract
The linear hypernetted chain approximation of Patey is inexact in the zero density limit. We examine this problem and suggest an alternative linearization of the hypernetted chain approximation that is exact at low densities. The new representation is readily extended to the quadratic hypernetted chain approximation and is applicable to any system of particles having cylindrical symmetry. By applying the new approximation to a dipolar system we are able to explore differences between the two approaches.
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