(63a) Experimental Validation of 2- and 3-Body Ab Initio Potentials for Helium-4 Via Second to Seventh Virial Coefficients

Authors: 
Gokul, N., University at Buffalo, The State University of New York
Kofke, D. A., University at Buffalo, The State University of New York
Schultz, A. J., University at Buffalo, The State University of New York
We examine the accuracy of virial coefficients Bn(T) for 4He for n = 2 to 7 and temperatures T
from 2 K to 1000 K, while reporting new values from semiclassical and (for n = 5) path-integral
Monte Carlo (PIMC) calculations. All coefficients are based on accurate first-principles 2- and 3-
body molecular models from the literature, and for n ≤ 5 have estimated stochastic and
systematic uncertainty between 0.005% to 20%, depending on n and T (almost all of this is due
to estimated inaccuracy in the 3-body potential) The calculated Bn(T) are used to examine the
virial equation of state (VEOS) against experimental data from the literature, from 223.15 K to
500 K and pressures up to 38 MPa. First, the VEOS is used to calibrate the data, providing
adjustments not exceeding the data’s estimated systematic uncertainty. Then, findings from the
comparison include: (1) the VEOS based on the ab initio Bn(T) is fully consistent with the
experimental data; (2) the series requires coefficients up to n = 5 in order to agree with
experiment within all relevant uncertainties; (3) individual values Bk(T) can be regressed
accurately from the experimental data if other coefficients Bn(T), n != k are given from the ab
initio calculations; however, the uncertainty of these values is less than the coefficient value only
for k ≤ 5. Having successfully validated the VEOS against high quality pressure measurements,
we check its performance in predicting critical properties as well as thermal properties including
specific heat and speed of sound.