Model for the Quantum Scattering of aHe3Impurity from a Rectilinear Vortex in Liquid He II

A model is given that describes the quantum scattering of a ${\mathrm{He}}^3$ impurity from a rectilinear vortex in liquid He II; the principal assumption is the existence of an impurity wave function that satisfies a Schrödinger equation. Various possibilities for the impurity-vortex interaction are discussed. For certain interactions, the theoretical results are consistent with the experimental work of Rayfield and Reif provided spatial variations in the superfluid density are considered. A $T$-matrix formalism is also developed and applied to the vortex scattering of impurities, as well as phonons and rotons. The results are compared to existing theoretical and experimental work; the main discrepancies occur for roton scattering.