Semiclassical fifth virial coefficients for improved ab initio helium-4 standards

For helium-4, we present ab initio, semiclassical calculations of virial coefficients B _n for n = 2, 3, 4, and 5 from 50 to 1000 K. Using our values of B ₄ and B ₅ and the more accurate literature values of B ₂ and B ₃, we argue that the ab initio virial equation of state is more accurate than recent, high-quality, densimeter measurements spanning the range {223 K < T < 500 K, p < 38 MPa}. Thus, the present values of B ₄ and B ₅ extend the useful temperature and density range of ab initio helium standards.