Path-integral calculation of the fourth virial coefficient of helium isotopes

摘要: We use the path-integral Monte Carlo (PIMC) method and state-of-the-art two-body three-body potentials to calculate fourth virial coefficients $D(T)$ of $^4$He $^3$He as functions temperature from 2.6K 2000K. derive expressions for contributions exchange effects due bosonic or fermionic nature helium isotope; these have been omitted previous calculations. The are relatively insignificant at temperatures considered, but they necessary quantitative accuracy below about 4K. Our results consistent with theoretical work (and some limited scattered experimental data) $^4$He; there no values this provides first calculated level. uncertainty depends on statistical PIMC calculation, estimated effect omitting four-body higher terms in potential energy, contribution propagated potentials. At low temperatures, is dominated by calculations, while high uncertainties related higher-order become dominant.