Theory of nuclear magnetic resonance line shapes for multispin systems containing a single quadrupolar nucleus

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Abstract
A theoretical expression for the high-resolution nuclear resonance band shape of a group of magnetically equivalent spin-½ nuclei weakly coupled to other magnetically equivalent groups of spin-½ nuclei and to one quadrupolar nucleus is derived using Redfield's relaxation theory. The detailed treatment is carried out with the assumption that molecular reorientation is sufficiently rapid for the extreme narrowing approximation to be applicable. It is found that the overall band shape is expressible as a sum of identical functions centred at the resonant frequencies calculated in the absence of the quadrupolar nucleus.