  We calculate the NMR relaxation rate due to quadrupolar coupling of the
nucleus to a local, strongly anharmonic phonon mode. As a model potential for a
rattling motion we consider a square-well potential. We calculate the free
phonon Green's function analytically and derive the low and high temperature
limits of the NMR relaxation rate. It is shown that the temperature dependence
of the NMR relaxation rate possesses a peak in contrast to harmonic phonons but
in qualitative agreement with a recent NMR study on KOs2O6. We discuss the
influence of phonon renormalization due to electron-phonon interaction.
