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

TL;DR

This paper presents highly accurate ab initio calculations of helium's third density and acoustic virial coefficients, significantly surpassing experimental precision and extending to very low temperatures, aiding in improved gas-based metrology.

Contribution

The study introduces new first-principles calculations of helium virial coefficients with unprecedented accuracy and extends the temperature range down to 0.5 K.

Findings

Uncertainty in third density virial coefficient reduced by factor of 4-5.

Calculated acoustic virial coefficients are consistent with experiments but with smaller uncertainties.

Data enables improved primary temperature and pressure measurements.

Abstract

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 $^4$He and $^3$He. 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 $\gamma_a(T)$, we applied the Schlessinger Point Method, which can calculate $\gamma_a$ and its uncertainty based on the $C(T)$ data, overcoming some limitations of direct path-integral calculation. The resulting $\gamma_a$ 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.