Path-integral calculation of the fourth virial coefficient of helium isotopes
Abstract
We use the path-integral Monte Carlo (PIMC) method and state-of-the-art two-body and three-body potentials to calculate the fourth virial coefficients of He and He as functions of temperature from 2.6K to 2000K. We derive expressions for the contributions of exchange effects due to the bosonic or fermionic nature of the helium isotope; these effects have been omitted from previous calculations. The exchange effects are relatively insignificant for He at the temperatures considered, but for He they are necessary for quantitative accuracy below about 4K. Our results are consistent with previous theoretical work (and with some of the limited and scattered experimental data) for He; for He there are no experimental values and this work provides the first values of calculated at this level. The uncertainty of the results depends on the statistical uncertainty of the PIMC calculation, the estimated effect of omitting four-body and higher terms in the potential energy, and the uncertainty contribution propagated from the uncertainty of the potentials. At low temperatures, the uncertainty is dominated by the statistical uncertainty of the PIMC calculations, while at high temperatures the uncertainties related to the three-body potential and to omitted higher-order contributions become dominant.
Keywords
Cite
@article{arxiv.2101.02624,
title = {Path-integral calculation of the fourth virial coefficient of helium isotopes},
author = {Giovanni Garberoglio and Allan H. Harvey},
journal= {arXiv preprint arXiv:2101.02624},
year = {2021}
}
Comments
13 pages, 3 figures. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Chem. Phys. 154, 104107 (2021) and may be found at https://doi.org/10.1063/5.0043446