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We derive path-integral expressions for the second and third virialcoefficients of monatomic quantum gases. Unlike previous work that consideredonly Boltzmann statistics, we include exchange effects (Bose-Einstein orFermi-Dirac statistics). We use state-of-the-art pair and three-body potentialsto calculate the third virial coefficient of 3He and 4He in the temperaturerange 2.6-24.5561 K. We obtain uncertainties smaller than those of the limitedexperimental data. Inclusion of exchange effects is necessary to obtainaccurate results below about 7 K.

Path-integral calculation of the third virial coefficient of quantum gases at low temperatures