Theory of ion mobility in liquid³He

Abstract

An ion interacting with quasiparticles in liquid³He is treated theoretically by summing most divergent terms in perturbation series of the self-energy of the ion and the vertex part. The ion Green's function is renormalized by a factorZ(T), and the vertex part byZ(T) ⁻¹, where${\text{Z(T)}} = {\text{(T/T}}_F {\text{)}}^{{\text{2V}}_{{\text{0}}^{\rho ^{\text{2}} } }^{\text{2}} }$, forT ₀≪T≪T _F. Here,T ₀=(m/M)T _F, withm the³He mass andM the ion mass, and${\text{V}}_{0^\rho }$ is the strength of the interaction. The factor explains the weak temperature dependence of the mobility around the minimum atT ₀; we also discuss its effect on the behavior of the mobility in³He-B nearT _c.