Variational calculation of ground-state properties of a binary boson system: Properties of dilute mixtures ofHe3atoms in superfluidHe4

In the theory of Woo, Tan, and Massey the properties of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are determined by ground-state properties of the corresponding binary boson system. Here, we present a variational calculation for these ground-state properties of the binary boson system as well as for the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixture. A correction to the long-wavelength effective interaction is calculated by a paired-phonon analysis using the ground-state wave function of pure liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The present results are consistent with other phenomenological theories. Particularly, the effective ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ quasiparticle interaction above about 7.4 atm is qualitatively in agreement with that obtained by Landau, Tough, Brubaker, and Edwards from osmotic-pressure data.