Multiple Spin Echoes in Dipolar Solids

The decay of transverse nuclear spin magnetization in a homogeneously broadened solid can be prolonged for a time ${T_2}^{†}\gg T_2$ by applying a train of 90° pulses in a modified Carr-Purcell sequence with pulse spacing $\tau <T_2$. A time-expansion theory which treats the problem from the viewpoint of spin echoes is used to explain an observed proportionality between ${T_2}^{†}$ and ${\tau }^{-5\mathrm{}}$, and predicts that ${T_2}^{†}$ depends upon a modified sixth moment of the resonance. An alternative viewpoint, in which one considers the long-time development of the spin system in a periodically modulated rf field $H_1\mathrm{}\left(t\right)\mathrm{}$, shows that the experiment is closely related to spin locking and explains the fact that ${T_2}^{†}\to T_{1\rho }\left({\overline{H}}_1\right)$, the relaxation time parallel to the average rf field, as $\tau \to 0$. The experiment offers some possibilities for the study of spin-lattice relaxation in weak fields and for double resonance in the rotating frame.