An Analysis of the Accuracy of the Calculation of the Second Virial Coefficient of Helium from Interatomic Potential Functions

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Abstract
In considering the second virial coefficient corrections for low temperature helium gas thermometry, the ITS-90 has incorporated data fits for the 4He and 3He second virial coefficients. An alternative is to use second virial coefficients calculated from recent interatomic potential functions for helium. We compare several functions using different computer codes to assess the accuracy of the calculations. The most recent function is the HFD-B2 of Aziz and Slaman. In the literature it is found that the potentials developed by different authors using their respective codes indicate a spread of only 0,4 cm3/mol at the lowest experimental temperature (2,6 K) for 4He. When calculations based on these same potentials are performed with the same code, the spread is nearly twice as large. However, calculations based on the two codes which have undergone recent improvements produce a spread of less than 0,01 cm3/mol when based on the same potential. For 3He, there is a relative difference between potential functions of 0,4 cm3/mol down to the lowest temperature of 1,5 K. There is a larger systematic difference between the calculations and the data fit which indicates that there is a contribution from the third virial in the latest 3He second virial coefficient data.