Equations of motion of nuclear magnetism in liquids in the presence of chemical exchange

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Abstract
The Zubarev non-equilibrium statistical operator formalism is applied to derive the phenomenological Hahn-Maxwell-McConnell equations (HMM equations). The derivation is based on the model according to which the Zeeman hamiltonian is modulated by chemical exchange and the operator of the total spin of nuclei in equivalent positions does not commute with the lattice hamiltonian. The scalar spin-spin interactions are assumed to be negligibly small. Conditions for the validity of the HMM equations are obtained. In particular, under extreme narrowing conditions, slightly modified HMM equations are valid regardless of the strength of the static or oscillating external magnetic field. A relation is obtained which expresses transfer rates in terms of time-dependent correlation functions. The time of transverse cross-relaxation due to the dipole-dipole interactions is also evaluated. This time determines the lowest exchange rates which can be measured by spin-echo experiments.