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Spin relaxation is due to fluctuating spin interactions. This chapter describes the relevant couplings in terms of their Hamiltonians. The most important interactions are dipolar couplings. Depending on the spin species, the system of interest and the experimental conditions, interactions of nuclear electric quadrupole moments with molecular electric field gradients, scalar and indirect spin–spin interactions and the influence of the anisotropy of the chemical shift tensor can also be efficient sources of relaxation. The Hamiltonians are discussed with respect to their dependence on spin operators and structural features of the spin-bearing molecules or molecular entities. Concerning spin operators, a distinction is made between secular and non-secular terms. Secular, i.e. spin energy-conserving, spin interactions are responsible for the so-called local fields and are an important source of transverse relaxation. This is in contrast to the non-secular counterparts on which spin–lattice relaxation is based.

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