Skip to main content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.


The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Path-Integral Calculation of the Second Dielectric and Refractivity Virial Coefficients of Helium, Neon, and Argon



Giovanni Garberoglio, Allan H. Harvey


We present a method to calculate dielectric and refractivity virial coefficients using the path-integral Monte Carlo formulation of quantum statistical mechanics and validate it by comparing our results with equivalent calculations in the literature and with more traditional quantum calculations based on wavefunctions. We use state-of-the-art pair potentials and polarizabilities to calculate the second dielectric and refractivity virial coefficients of helium (both 3He and 4He), neon (both 20Ne and 22Ne), and argon. Our calculations extend to temperatures as low as 1 K for helium, 4 K for neon, and 50 K for argon. We estimate the contributions to the uncertainty of the calculated dielectric virial coefficients for helium and argon, finding that the uncertainty of the pair polarizability is by far the greatest contribution. Agreement with the limited experimental data available is generally good, but our results have smaller uncertainties, especially for helium. Our approach can be generalized in a straightforward manner to higher-order coefficients.
Journal of Research (NIST JRES) -


argon, dielectric virials, helium, neon, path-integral Monte Carlo, pressure, refractivity virials, thermometry
Created August 5, 2020, Updated August 6, 2020