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The second virial coefficient and the second acoustic virial coefficient forhelium-4 and helium-3 are computed for a wide range of temperatures (0.5 -1000K) using a highly accurate nonrelativistic interaction potential [M.Przybytek et al., Phys. Rev. Lett. 119, 123401 (2017)] and recalculatedrelativistic and quantum-electrodynamic components. The effects of thelong-range retardation and of the nonadiabatic coupling of the nuclear andelectronic motion are also taken into account. The results of our calculationsrepresent at least fivefold improvement in accuracy compared to the previous abinitio work. The computed virial coefficients agree well with the most accuraterecent measurements but have significantly smaller uncertainty.

Second virial coefficients for helium-4 and helium-3 from accurate relativistic interaction potential