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Interacting hard-sphere fluids in an external field

We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary shape and limited range. Our method of analysis is exact in one dimension and provides demonstrably good approximations in higher dimensions. It can cope with homogeneous and heterogeneous environments. We derive an equation for the pair distribution function. The solution, to be evaluated numerically, in general, or analytically for special cases, enters expressions for the entropy and free energy functionals. For some one-dimensional systems, our approach yields analytic solutions, reproducing available exact results from different approaches.