Nonexponential Relaxation of Three-Spin Systems in Nonspherical Molecules

The longitudinal and transverse nuclear magnetic relaxation of a system of three identical spin-12 nuclei in equivalent positions at the corners of an equilateral triangle fixed perpendicular to the axis of a symmetric-top molecule is calculated on the assumptions that :(1) The relaxation is due to the dipole–dipole interactions between the three spins, including the effects of cross correlations, (2) the motion of the molecule can be treated as anisotropic rotational Brownian motion, and (3) the correlation time is short. The relaxation is found to be the sum of two decaying exponentials. The deviation from a simple exponential decay is greatest when the rotational diffusion about the symmetry axis is rapid compared to the rotational diffusion about an axis perpendicular to the symmetry axis.