Variational study ofHe3-He4mixtures

The ground-state properties of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixture are investigated by assuming the wave function to be a product of pair correlations. The antisymmetry of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ component is taken into account by Fermi-hypernetted-chain techniques and the results are compared with those obtained from the lowest-order Wu-Feenberg expansion and the boson-boson approximation. A little improvement is found in the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ maximum solubility. A microscopic theory to calculate ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ static properties such as zero-concentration chemical potential and excess-volume parameter is derived and the results are compared with the experiments.