Path Integral Monte Carlo Simulation of Isotopic Liquid Helium Mixtures

We report results of a path integral Monte Carlo simulation of a liquid ${}^3\mathrm{He}$- ${}^4\mathrm{He}$ mixture at low temperature. In the limit of low ${}^3\mathrm{He}$ concentration, a kinetic energy of 17 K is found for the ${}^3\mathrm{He}$ atoms; the ${}^3\mathrm{He}$ effective mass is $m^{*}=2.3m$. The restricted path integral Monte Carlo method was utilized to investigate the separation of the mixture into a ${}^3\mathrm{He}$- and ${}^4\mathrm{He}$-rich phase.