Sixth and Eighth Moments of the Magnetic-Resonance Lines of a Dipolar-Coupled Rigid Lattice

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Abstract
Analytical expressions for the sixth and eighth moments of the magnetic-resonance lines of a dipolar-coupled rigid lattice are obtained by performing the commutations of angular momentum operators and the necessary reductions by means of a computer. The expressions are used to derive numerical values of the moments for a simple cubic lattice for varying numbers of interacting neighbors. The sixth and eighth moments predicted from Abragam's trial function for the free-induction-decay curve are compared to the corresponding exact moments reported here. We also present a straightforward method for the algebraic computer calculation of traces of angular momentum operators.