Sixth Moment of Dipolar-Broadened Magnetic-Resonance-Absorption Line Shapes in Crystals

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Abstract
Several recently developed theories of broad-line NMR presume the knowledge of the first several moments of the line shape. An exact expression for the sixth moment for the purely dipolar-broadened case is presented here. The result indicates that the sixth moment consists of one type of two-particle term, five types of three-particle terms, and nine types of four-particle terms, one of which has a vanishing coefficient. Most of the contribution comes from the four-particle terms.