Multiple Spin Echoes in Dipolar Solids

Abstract

The decay of transverse nuclear spin magnetization in a homogeneously broadened solid can be prolonged for a time ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\gg}{T}_{2}$ by applying a train of 90\ifmmode^\circ\else\textdegree\fi{} pulses in a modified Carr-Purcell sequence with pulse spacing $\ensuremath{\tau}<{T}_{2}$. A time-expansion theory which treats the problem from the viewpoint of spin echoes is used to explain an observed proportionality between ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}$ and ${\ensuremath{\tau}}^{\ensuremath{-}5}$, and predicts that ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}$ 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 ${H}_{1}(t)$, shows that the experiment is closely related to spin locking and explains the fact that ${{T}_{2}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\rightarrow}{T}_{1\ensuremath{\rho}}({\overline{H}}_{1})$, the relaxation time parallel to the average rf field, as $\ensuremath{\tau}\ensuremath{\rightarrow}0$. The experiment offers some possibilities for the study of spin-lattice relaxation in weak fields and for double resonance in the rotating frame.