Virial series for fluids of hard hyperspheres in odd dimensions

Abstract

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) d dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients Bj are expressed in terms of the solution of a set of (d-1) /2 coupled algebraic equations which become nonlinear for d5. Results have been derived up to d=13. A confirmation of the alternating character of the series for d5, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension 2 1/d, where is the packing fraction, is wholly consistent with the limiting value of 1 for d→∞. Finally, the values for Bj predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)].