Ultra-accurate thermophysical properties of helium-4 and helium-3 at low density. I. Second pressure and acoustic virial coefficients

The second pressure and acoustic virial coefficients of helium-4 and helium-3 are computed employing an accurate <i>ab initio</i> potential from the literature. The fully quantum-mechanical formulations are derived for second acoustic virial coefficient, which are not available in the literature. The uncertainty of our calculated values is quantified and evaluated based on the potential inaccuracy. For helium-4, our theoretical values are in excellent agreement with the best measurements and a recent <i>ab initio</i> calculation. Our estimated uncertainty is at least five times smaller than the previous best determination. For helium-3, systematic errors are detected for the widely accepted <i>ab initio</i> data and our new results are probably more reliable. The computed values of this work are given in the supplemental materials over a wide temperature range between 1 and 10 000 K, which are useful especially for primary temperature metrology.