Averaging of transverse relaxation times of scalar coupled nuclei under spin lock conditions

Abstract

The response of a scalar coupled spin system to a train of closely spaced 180° pulses is analyzed by means of an effective Liouville operator from which terms involving chemical shifts are omitted. It is shown that the resulting equations of motion for the spin density matrix are most easily solved in a basis for which the spin coupling part of the Hamiltonian is diagonal. Transverse relaxation behavior for each line in the spectrum may then be calculated by transforming to the basis in which the entire time independent Hamiltonian is diagonal. The analysis shows that under spin lock conditions produced by rapid nonselective pulses, the existence of scalar coupling causes all transitions of the same symmetry to exhibit identical transverse relaxation behavior. For two coupled nuclei of spin 1/2 all four transitions are shown to decay with the same single exponential, and the relaxation time is the average of relaxation times expected for each spin in the absence of scalar coupling. Experimental results demonstrating this averaging effect are reported for the protons in neat 2,3-dibromothiophene.