Theory of aHe3Atom in LiquidHe4atT=0

Abstract

The problem of a single ${\mathrm{He}}^3$ atom in liquid ${\mathrm{He}}^4$ is formulated, interaction matrix elements evaluated, the approximate formula for the energy solved numerically, and numerical results for the separation energy, effective mass, and differential volume coefficient compared with experimental information. Second order corrections to the differential volume coefficient $\alpha$ are found to be almost negligible (<5%); consequently, the experimental $\alpha \left(\rho \right)$ gives direct and moderately accurate information on the mean kinetic energy of the boson liquid as a function of density.