Theory of Binary Boson Solutions

Abstract

The properties of a dilute solution of mass-3 bosons in liquid ${\mathrm{He}}^{4}$ at low temperatures are computed via a variational procedure. A set of coupled integrodifferential equations is solved, yielding expressions for the ground-state energy per particle, the binding energy of ${\mathrm{He}}^{3}$ in ${\mathrm{He}}^{4}$, the (3, 3), (4, 3), and (4, 4) distribution functions, and the long-wavelength limit of the effective interaction between ${\mathrm{He}}^{3}$ quasiparticles in ${\mathrm{He}}^{4}$. Numerical results are obtained and compared with experiment.