Equation of state of hard and Weeks-Chandler-Anderson hyperspheres in fourand five dimensions

The fifth and sixth virial coefficient for hard hyperspheres in four and fi ve dimensions has been computed using Monte Carlo techniques. It is found t hat B-5/B-2(4) has values 0.035 63+/-0.000 07 and 0.012 87+/-0.000 06 and t hat B-6/B-2(5) has values 0.007 691+/-0.000 028 and 0.000 942+/-0.000 027 i n four and five dimensions, respectively. These values are used to investig ate the equation of state of hard and Weeks-Chandler-Anderson (WCA) hypersp heres in four and five dimensions. Molecular dynamics simulations are perfo rmed for WCA hyperspheres. When compared to the molecular dynamics calculat ions, it is found that both the hard hypersphere and WCA equations of state are well described by a variety of theoretical approaches as long as the d ensity is in the low-to-moderate regime. At the highest fluid densities stu died, the Luban-Michels procedure provides the best accuracy for hard hyper spheres. The WCA prescription for the scaling of the reference system to a hard hypersphere one is a very good approximation in the fluid region. (C) 1999 American Institute of Physics. [S0021-9606(99)51223-3].