Lattice Relaxation in Solid He-4: Effect on Dynamics of He-3 Impurities

We present a new simplified derivation of the effect of lattice relaxation that accompanies the quantum tunneling of He-3 impurities in solid He-4 on the nuclear spin-lattice relaxation of the He-3 impurities for very low impurity concentrations. As a result of the larger zero point motion of the He-3 impurity compared to the He-4 atoms, a significant lattice distortion accompanies the impurity as it moves through the lattice and the dynamics of the impurity depends on both the interaction energy between two He-3 atoms and on the relaxation of the lattice for the tunneling impurity. Using a phenomenological model for the lattice relaxation we compare the nuclear spin-lattice relaxation rates observed at low temperatures with the dependence on temperature expected for a He-4 lattice relaxation comparable to that observed by Beamish et al. (Phys. Rev. Lett. 96:195304, 2006).