Effect of Dipolar Cross Correlations on the Transverse Relaxation of Single- and Multiple-Quantum Coherences in Strongly Coupled Spin Systems

The effect of dipolar cross correlations and strong coupling in transverse relaxation of single- and multiple-quantum coherences is investigated for a homonuclear ABX spin system. Analytical expressions for the linewidth of each coherence, in the limit of the simple-line approximation, have been obtained by explicit calculation of the spectral densities at frequencies zero, $\omega$, and $2\omega$, where $\omega$ is the Larmor frequency. The results are presented in a matrix notation which clearly separates the contribution of auto- and cross-correlation spectral densities as well as the contribution of strong coupling to these linewidths. It is found that, in the strong-coupling situation, all the coherences between mixed eigenstates have unequal linewidths in the presence as well as in the absence of cross correlations. In the weak-coupling limit, the cross correlations show up as a differential effect to the linewidths such that single-quantum coherences among themselves and the double- and zero-quantum coherences taken together have equal numbers of cross terms with positive and negative sign. In the strong-coupling limit, cross correlations also contribute a net effect to these linewidths. The triple-quantum coherence has a contribution from cross correlations but not from strong coupling