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

We present a new simplified derivation of the effect of lattice relaxation that accompanies the quantum tunneling of 3He impurities in solid 4He on the nuclear spin-lattice relaxation of the 3He impurities for very low impurity concentrations. As a result of the larger zero point motion of the 3He impurity compared to the 4He 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 3He 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 4He lattice relaxation comparable to that observed by Beamish et al. (Phys. Rev. Lett. 96:195304, 2006).