Monte Carlo study of liquidHe3-He4solutions

The ground state of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ solution was represented by a Jastrow wave function times Slater determinants for the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms, and a Monte Carlo calculation was performed for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ concentrations of 6.5, 12, and 44 at.%. The average binding energy per atom, the radial distribution functions, the structure functions, the momentum distribution of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atoms, and the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ condensate fraction $n_0$ were calculated. In the above concentrations, the values of $n_0$ were found to be 13.1±1%, 13.7±1%, and 19.0±1%, respectively, compared to 11% for bulk liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. This enhancement of $n_0$ is due mainly to the decreasing density of the solution as the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ concentration increases. Similar calculations were done for mass-3—mass-4 boson solutions. The radial distribution function of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ solution are different from those of the mass-3—mass-4 boson solutions due to the difference in statistics.