Path-integral calculation of the third dielectric virial coefficient of helium based on ab initio three-body polarizability and dipole surfaces

TL;DR

This paper calculates the third dielectric virial coefficient of helium using ab initio three-body polarizability and dipole surfaces, providing more accurate data for temperature and pressure measurements.

Contribution

It introduces a new surface for the helium three-body dipole moment and rigorously propagates uncertainties to improve virial coefficient accuracy.

Findings

Results agree with previous data using approximate methods.

Extended calculations to low temperatures including exchange effects.

Uncertainty in $C_\varepsilon$ is quantified and found to be significant.

Abstract

We develop a surface for the electric dipole moment of three interacting helium atoms and use it, together with state-of-the-art potential and polarizability surfaces, to compute the third dielectric virial coefficient, $C_\varepsilon$, for both $^4$He and $^3$He isotopes. Our results agree with previously published data computed using an approximated form for the three-body polarizability, and are extended to the low-temperature regime by including exchange effects. Additionally, the uncertainty of $C_\varepsilon$ is rigorously determined for the first time by propagating the uncertainties of the potential and polarizability surfaces; this uncertainty is much larger than the contribution from the dipole-moment surface to $C_\varepsilon$. Our results compare reasonably well with the limited experimental data. The first-principles values of $C_\epsilon$ computed in this work will enhance the accuracy of primary temperature and pressure metrology based on measurements of the dielectric constant of helium.