For the three-dimensional hard-sphere model we investigate the inhomogeneous two-body correlations predicted by Rosenfeld's fundamental measure theory. For the special cases in which the density has either planar or spherical symmetry we provide analytic formulas for the Hankel and Legendre transforms, respectively, of the inhomogeneous two-body direct correlation function as explicit functionals of the density. When combined with the Ornstein-Zernike relation our analytical results allow for rapid calculation of inhomogeneous hard-sphere density correlations in real space. These not only provide information about the packing structures of the hard-sphere system but also form an essential building-block for constructing perturbation theories of more realistic models.

• Received 22 January 2021
• Accepted 25 February 2021

DOI:https://doi.org/10.1103/PhysRevE.103.042103