Something more about relaxation rates

After the perturbation, the system tends to reach equilibrium again. We assume that the return to equilibrium is a stochastic process, i.e. each step towards equilibrium is random and uncorrelated to other steps. This implies that the spins are not related one to the other. Under these conditions the return to equilibrium is a first order kinetic process. The decay, as in Eq. (1.42), is then given by 

The magnetic field has cylindrical symmetry, i.e. the physical properties of a system do not change upon rotation about the field direction, and there is no difference between x and y directions. If the measurement of the return to equilibrium is performed along the Bq direction, i.e. the return to equilibrium 

In a typical experiment, called inversion recovery, Mz is initially inverted by applying a 180° pulse. Its recovery along the z axis is given by 

All the mechanisms which contribute to R contribute also to R2, because the re-establishment of the equilibrium population brings zero magnetization in the xy plane. The dephasing, or fanning out, of the single spin components in the xy plane contributes only to / 2. Therefore 

The presence of unpaired electrons will activate new relaxation pathways, and 

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