Theory of Dilute Solutions ofHe3in LiquidHe4

Abstract

A perturbative calculation in the correlated representation is carried out in full for dilute solutions of ${\mathrm{He}}^3$ in liquid ${\mathrm{He}}^4$. The theory begins with bare atoms and realistic potentials and derives from first principles the effective mass of ${\mathrm{He}}^3$ quasiparticles and the effective interactions between them. It contains no adjustable parameter, and thus, provides a definite microscopic foundation for the Bardeen-Baym-Pines phenomenological model. Numerical evaluations result in an effective mass of $2.37m_3$ and an effective interaction in qualitative agreement with that determined by Baym and Ebner.