Dynamics of ${ }^3$He Impurities in Solid ${ }^4$He near the Apparent Supersolid Transition

We report measurements of the nuclear spin-spin and nuclear spin-lattice relaxation times for ${ }^3$He impurities in solid hcp ${ }^4$He for a molar volume of 21 cm$^3$. The ${ }^3$He concentrations range from 20 to 2000 ppm and the relaxation times were measured for temperatures 1.4 K$>$T$>$0.010 K. The results are discussed in terms of the dynamics of the ${ }^3$He impurities and their scattering by other impurities and by other defects. In addition we report new results for the phase separation of the ${ }^3$He from the ${ }^4$He and the formation of ${ }^3$He nanodroplets in the solid ${ }^4$He matrix.