Diffusion of Dilute He³ Impurities in Solid He⁴

Abstract

It is expected that a He³ atom in solid He⁴ travels through the lattice due to the tunneling effect and behaves as a quasi-particle, “impuriton”. We calculate the spin diffusion coefficient D of impuritons, using a realistic interaction between impuritons and obtain D\simeq(J₃₄a)²⁄xV₀, where J₃₄ is the He³–He⁴ exchange constant, a the lattice constant, x the concentration of He³ impurities and V₀ the strength of the interaction. It is shown that J₃₄ is the same order of magnitude as the He³–He³ exchange constant in pure He³ solid at the same molar volume.