Nuclear-Magnetic-Resonance Line Shape in Solids

Abstract

The method of retarded Green's functions is applied to the calculation of rigid-lattice dipolar line shapes in solids. Some familiar results are derived for the case of isolated spins and spin pairs. The case of $N$ inter-acting spins is also considered. An expression for the line shape is obtained by employing a frequency-dependent decoupling approximation. Simple constant decoupling approximations do not lead to damped line shape functions. The result is compared with early experimental data obtained by Bruce on the ${\mathrm{F}}^{19}$ resonance in a single crystal of calcium fluoride. The theoretical free induction decays obtained by Fourier-transforming the line shape are also compared with experimental data from Lowe and Norberg. The line shape derived is strongly dependent on the ratio of the fourth moment to the square of the second moment. Increases of this ratio, corresponding to inclusion of exchange interactions, are shown to produce dramatic narrowing of the absorption line, which ultimately approaches a Lorentzian function.