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 F¹⁹ nuclei in a fluorite (CaF₂) 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 CaF₂ thus corresponds to the calculation of the shape of the F¹⁹ resonance line for the crystal. It is demonstrated that the resonance line shape for an ordered rigid lattice is not Gaussian.
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Lowe et al. (1957) studied this question.
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