Virial coefficients for hard discs and hard spheres

The sixth, seventh and eighth virial coefficients of hard discs and hard spheres are evaluated numerically (Monte Carlo integration). I improve on the best previous estimates for the seventh virial coefficients, and the integration of the eighth virial coefficient is new. The best estimates for these coefficients for hard discs are B 7 /b 6 = 0.114 86(7) and B 8 /b 7 = 0.065 14(8); and for hard spheres B 7 /b 6 = 0.01307(7) and B 8 /b 7 = 0.00432(10). b is the second virial coefficient in each case. Pade approximations to the excess pressure and the excess free energy are computed from these results and compared to data otherwise obtained.