Fundamental measure theory of inhomogeneous two-body correlation functions

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