Quantum Liquids. II. Microscopic Theory of LiquidHe3-He4Mixtures

Abstract

We calculate the equilibrium and transport properties of the mixtures using the overcomplete basis functions ${\varphi }^k{\psi }_q$ discussed in I. The theory includes the enlarged correlation hole of a single ${\mathrm{He}}^3$ and the backflow of ${\mathrm{He}}^4$ atoms around it. The two quasiparticle scattering amplitude is the sum of two terms $V=-{\alpha }^2\frac{m_4{s}^2}{n}-\frac{{\hslash }^2\left(\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{q}}\right)\left({\overrightarrow{\mathrm{k}}}^{\prime }·\overrightarrow{\mathrm{q}}\right)}{m_{4}n{q}^2}{\left(\frac{(1+\alpha )m_4+\delta m}{m_3+\delta m}\right)}^2$ the first from the interaction of the excess correlation holes and the second from the interaction of the backflows. Both terms were derived previously from macroscopic considerations by Bardeen, Baym, and Pines.