Relaxation-induced oscillations of spin-echo envelopes

In scalar-coupled spin systems where in-phase and antiphase coherences have different lifetimes, the envelopes of spin echoes may feature modulations that are induced by relaxation. These modulations are most pronounced when the couplings that lead to the interconversion of in-phase and antiphase coherences are too small to provide an effective mechanism for averaging. The modulations occur even if the scalar coupling term is formally eliminated from the average Hamiltonian that describes the evolution between initial excitation and the time of the echo. The frequency of the relaxation-induced oscillations is one-half of the scalar coupling constant, and the modulation depth is determined by the ratio between the difference in relaxation rates of the in-phase and antiphase coherences and the scalar coupling.