Magnetic Resonance Line Shapes in Solids: The Rotating Three-Spin Group

The density matrix formalism of spin-exchange theory has been applied to the problem of a rigid equilateral triangle of spin-1 / 2 nuclei undergoing random hindered rotation about the normal to the plane of the triangle. The resulting equations were solved numerically, and spectra are presented for a variety of rates of rotation for both a single orientation and a sum over orientations. These results are compared with recent calculations for coherent rotation (tunneling) of methyl groups, and the experimental situation is briefly discussed.