The first Born-Green equation for an inhomogeneous fluid, which relates the density profile and an integral of the pair distribution of the fluid, is solved for the particular case of a system of hard spheres near a hard wall. The recent approximation of Henderson and Plischke, which is constructed from the Kirkwood superposition approximation and the Percus shielding approximation, is used for the pair distribution function. The results for the density profile are in reasonably good agreement with Monte Carlo simulations; they are very good near the wall but at larger distances are slightly worse than earlier analytic results obtained from the less sophisticated singlet theory which does not involve the inhomogeneous fluid pair correlation function.
Volume 134, 2022
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