Effect of tunneling on the frequency dependence and time evolution of nuclear magnetization in the rotating frame

The proton spin-lattice relaxation time in the rotating frame of a N${\mathrm{H}}_4$ group embedded in a crystal lattice is calculated. The effect of the N${\mathrm{H}}_4$-group tunneling is incorporated on the basis of a phenomenological model introduced by Clough and Punkkinen. It is shown that, in general, the magnetization decays with five time constants. If tunneling is very large, ${\omega }_T\gg \gamma H_0$, the magnetization decays in the rotating frame with one time constant. Search for large tunneling frequencies by varying the Larmour frequency at a constant spin-locking field $H_1$ is thus easier in the rotating frame than at high field. If tunneling splitting is small, ${\omega }_T\sim \gamma H_1$, the relaxation rate shows maxima whenever ${\omega }_T=2\mathrm{}\gamma H_1$, in good accord with experiment.