Relaxation Processes in a System of Two Spins

Abragam and Pound's method for the calculation of the longitudinal relaxation time $T_1$ has been extended to the transverse relaxation time $T_2$. Explicit calculations have been carried out for a pure dipole-dipole interaction, showing that for an interacting pair of like spins, or for nuclei in paramagnetic solution, $T_1$ is exactly equal to $T_2$ in the extreme narrow case. For a pair of interacting unlike spins, it is shown that the longitudinal components of the magnetic moments do not have simple exponential decays. This gives rise to a steady and transient Overhauser effect. The transverse components, however, have in all cases, simple exponential decay defined by a single relaxation time $T_2$. A set of modified Bloch's equations is found, giving the correct equation of motion of the macroscopic magnetic moments of such a system of pairs of unlike spins.