NMR pulse response and measurement of the quadrupole coupling constant of I=3/2 nuclei

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Abstract
The rf pulse response of a system of I=3/2 nuclei which experience identical first‐order quadrupole splitting is investigated using the density matrix method. A general expression is derived for the time evolution of the in‐phase magnetization following a rectangular pulse applied at the center line frequency. The maximum amplitude of the magnetization associated with the center line, and the length of pulse that gives rise to it, are calculated as a function of the ratio of the quadrupole splitting to the amplitude of the rf field. Data obtained for 23Na in a single crystal of NaNO3 are in fairly good agreement with the theoretical form. The theory has been extended to the case where the nuclei are situated at equivalent sites in a polycrystalline sample. The length of pulse that maximizes the amplitude of the FID of 23Na in a powder sample of NaNO3 has been measured as a function of the amplitude of the rf field. The quadrupole coupling constant, found by fitting the data to the theoretical form, is in very good agreement with the accepted value. It is proposed that this method can be widely used to measure the quadrupole coupling constants of I=3/2 nuclei.