Introduction to Nuclear Spin Cross-relaxation and Cross-correlation Phenomena in Liquids

This chapter deals with nuclear spin relaxation phenomena. It is, however, limited to nuclei of spin 1/2. It starts with a semi-classical survey of the relaxation mechanisms and the so-called ‘spectral densities’ in terms of which will be expressed for all relaxation parameters. To go further, the fundamentals of spin 1/2 quantum mechanics are presented with an emphasis on the so-called ‘product-operators’. Within the Bloch–Wangsness–Redfield theory, it is explained how the various spin states can be coupled by relaxation parameters, this coupling terms being arranged in the so-called ‘relaxation matrix’. The relaxation parameters include the classical relaxation rates (inverse of T₁ and T₂) and the cross-relaxation and cross-correlation rates. An original method, based on product-operators and spherical harmonics, leads, in a straightforward manner, to the calculation of the elements of the relaxation matrix.