Avoiding Interpolation Errors for Computed Second
Virial Coefficients of Noble Gases
Allan H. Harvey
Applied Chemicals and Materials Division, National Institute of Standards and
Technology, Boulder, Colorado, 80305-3337, USA
E-mail: allan.harvey@nist.gov
Giovanni Garberoglio
European Centre for Theoretical Studies in Nuclear Physics and Related Areas
(FBK-ECT*), Trento, I-38123, Italy
E-mail: garberoglio@ectstar.eu
20 August 2025
Abstract. Virial coefficients for noble gases calculated from first principles play a
key role in gas-based temperature and pressure metrology. They have typically been
presented in tabular form, but as smaller uncertainties are achieved the uncertainty
introduced by interpolation between tabulated points can become significant. We
demonstrate these interpolation errors for the second density and acoustic virial
coefficients of
4
He and for the second density virial coefficients of Ne and Ar. We
then offer an alternative approach, using simple scripts along with a data structure
containing precalculated phase shifts to generate these coefficients at any temperature
of metrological interest. The approach is applied to the state-of-the-art pair potentials
for
3
He,
4
He, Ne, and Ar, and the software and data tables are made available for
general use.
Keywords: argon; helium; interpolation; neon; phase shifts; second virial coefficents;
uncertainty
Revision submitted to Metrologia.
