The contact values gij(σij) of the radial distribution functions
of a d-dimensional mixture of (additive) hard spheres are considered. A
`universality' assumption is put forward, according to which
gij(σij)=G(η,zij), where G is a common function for all
the mixtures of the same dimensionality, regardless of the number of
components, η is the packing fraction of the mixture, and zij is a
dimensionless parameter that depends on the size distribution and the diameters
of spheres i and j. For d=3, this universality assumption holds for the
contact values of the Percus--Yevick approximation, the Scaled Particle Theory,
and, consequently, the Boublik--Grundke--Henderson--Lee--Levesque
approximation. Known exact consistency conditions are used to express
G(η,0), G(η,1), and G(η,2) in terms of the radial distribution
at contact of the one-component system. Two specific proposals consistent with
the above conditions (a quadratic form and a rational form) are made for the
z-dependence of G(η,z). For one-dimensional systems, the proposals for
the contact values reduce to the exact result. Good agreement between the
predictions of the proposals and available numerical results is found for
d=2, 3, 4, and 5.Comment: 10 pages, 11 figures; Figure 1 changed; Figure 5 is new; New
references added; accepted for publication in J. Chem. Phy