Interaction potential of a 3He atom in a superfluid 4He background.

Abstract

The deformation of the superfluid $^{4}\mathrm{He}$ ground state caused by the presence of a $^{3}\mathrm{He}$ atom is described in terms of a polaron model. The parameters of the model are derived from the experimentally known spectrum of the $^{4}\mathrm{He}$ elementary excitations and the static structure factor of $^{4}\mathrm{He}$. The resulting effective mass of the $^{3}\mathrm{He}$ atom is calculated with the Feynman path-integral technique, and compares well with the experimental $^{3}\mathrm{He}$ effective mass, on the condition that a microscopic $^{3}\mathrm{\ensuremath{-}}^{4}$He interatomic potential is used that is consistent with the static $^{4}\mathrm{He}$ structure factor. The main result of this paper is that the interatomic interaction potential, as, e.g., realized in the hypernetted-chain approach, leads to an accurate description of the deformation cloud around the $^{3}\mathrm{He}$ atom.