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We employ state-of-the-art pair and three-body potentials with path-integral Monte Carlo (PIMC) methods to calculate the third density virial coefficient C(T) for helium. The uncertainties are much smaller than those of the best experimental results, and approximately one-fourth the uncertainty of our previous work. We have extended our results in temperature down to 2.6 K, incorporating the effect of spin statistics that become important below approximately 7 K. Results are given for both the (3)He and (4)He isotopes. We have also performed PIMC calculations of the third acoustic virial coefficient γ a; our calculated values compare well with the limited experimental data available. A correlating equation for C(T) of (4)He is presented; differentiation of this equation provides a reliable and simpler way of calculating γ a.

Improved first-principles calculation of the third virial coefficient of helium