Third density and acoustic virial coefficients of helium isotopologues from ab initio calculations

Improved two-body and three-body potentials for helium have been used to calculate from first principles the third density and acoustic virial coefficients for both ^4He and ^3He. For the third density virial coefficient C(T), uncertainties have been reduced by a factor of 4–5 compared to the previous state of the art; the accuracy of first-principles C(T) now exceeds that of the best experiments by more than two orders of magnitude. The range of calculations has been extended to temperatures as low as 0.5 K. For the third acoustic virial coefficient γ_a(T), we applied the Schlessinger Point Method, which can calculate γ_a and its uncertainty based on the C(T) data, overcoming some limitations of direct path-integral calculation. The resulting γ_a are calculated at temperatures down to 0.5 K; they are consistent with available experimental data but have much smaller uncertainties. The first-principles data presented here will enable improvement of primary temperature and pressure metrology based on gas properties.