The path to relaxation

The fundamental requirement for longitudinal relaxation of a spin- /a nucleus is a time-dependent magnetic field fluctuating at the Larmor frequency of the nuclear spin. Only through this can a change of spin state be induced or, in other words, can relaxation occur. Local magnetic fields arise from a 

Molecular motion is therefore fundamental to the process of relaxation, but it remains to be seen how the fields required for this arise and how these mechanisms influence observed spectra. 

The most important relaxation mechanism for many spin- /2 nuclei arises from the dipolar interaction between spins. This is also the source of the tremendously important nuclear Overhauser effect and further discussions on 

The electron distribution in chemical bonds is inherently unsymmetrical or anisotropic and as a result, the local field experienced by a nucleus, and hence its chemical shift, will depend on the orientation of the bond relative to the applied static field. In solution, the rapid tumbling of a molecule averages this chemical shift anisotropy (CSA) such that one observes only a single frequency for each chemically distinct site, sometimes referred to as the isotropic chemical shift. Nevertheless, this fluctuating field can stimulate relaxation if sufficiently strong. This is generally the case for nuclei which exhibit a large chemical shift 

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Figure 5.21 Energy distribution of the Ms states for S = 10 and D = —0.5 cm in zero (left) and +3 T (middle) applied field along the molecular z axis, with illustration of equilibrium population distributions assuming only the lowest states are populated. (Right) Population distribution immediately after saturation at +3 T then removal of the field. The arrows indicate the path to relaxation via absorption then emission of thermal energy (phonons) from/to the lattice...

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