Free-Induction Decays in Solids

A beat structure has been found on free-induction decays associated with the pulsed nuclear magnetic resonance of nuclei in rigid lattices. A general quantum-mechanical theory is developed for the shapes of induction decays. The theory is specialized to the case of rigid solids and applied to the magnetic dipolar interactions among the ${\mathrm{F}}^{19}$ nuclei in a fluorite (Ca${\mathrm{F}}_2$) crystal. It is also shown rigorously that, except at very low temperatures, a free-induction decay is the Fourier transform of the corresponding steady-state resonance line shape. The calculation of the shape of an induction decay in Ca${\mathrm{F}}_2$ thus corresponds to the calculation of the shape of the ${\mathrm{F}}^{19}$ resonance line for the crystal. It is demonstrated that the resonance line shape for an ordered rigid lattice is not Gaussian.