Virial coefficients of hard spheres and hard disks up to the ninth -: art. no. 021105

A technique for topological analysis of the Ree-Hoover diagrams is developed with the aim to calculate the Ree-Hoover weights up to the ninth order with moderate demands on computer storage and CPU time. The ninth virial coefficients of hard spheres and disks are calculated, and the lower virial coefficients are accurately recalculated. The calculations require several spanning diagrams; the most important spanning chains are generated by reptation, other spanning diagrams by the standard Metropolis Monte Carlo algorithm. The tenth and eleventh virial coefficients for hard spheres are estimated.