Thermodynamics of a Fluid of Hard D-dimensional Spheres: Percus-Yevick and Carnahan-Starling-like Results for D = 4 and 5

The equations of state (EOS) of four and five dimensional hyperspheres have been calculated using Leutheusser's ansatz. In five dimensions these, and the correlation functions, are compared with the results obtained from the analytic solution of the Percus—Yevick (PY) approximation. It is shown that the ansatz reproduces extremely well the PY results. However, in both approximations neither the virial, Zv , nor the compressibility, Zc , EOS reproduce well the available molecular dynamics (MD) results. Yet a linear combination of Zv and Zc , following the Carnahan—Starling EOS for hard spheres, are in excellent agreement with the MD results in four and five dimensions.