Low temperature quantum diffusion of muonium in KCl

T ₁ spin relaxation of muonium in KCl has been studied at low temperatures (20 mK to 2 K), where the motion is believed to be band-like, i.e. the mean free path is longer than the lattice constant. The Celio model, based on the assumption of stochastic hopping of muonium, accurately describes the field dependence ofT ₁ at higher temperatures but fails below 4 K. The measuredT ₁ spin relaxation rates vary weakly with temperature below 2 K even thoughk _BT at the lowest temperature is well below the estimated muonium bandwidth obtained from the data at higher temperatures. This is taken as evidence that muonium is not completely thermalized on the time-scale of the muon lifetime due to the weak interaction with phonons at low temperatures.