UNIFIED DERIVATION OF THE DIPOLAR FIELD AND RELAXATION TERMS IN THE BLOCH-REDFIELD EQUATIONS OF LIQUID NMR

The standard theory of NMR relaxation in liquids (with molecular motio n described as a classical Brownian motion, and including intermolecul ar spin-spin couplings) is re-examined taking great care not to drop s ignificant contributions from the dipolar coupling between distant mol ecules. This results in ''modified Bloch-Redfield equations'' for the spins in a single molecule, valid at all spin temperatures, which cont ain both the usual relaxation terms and a coupling of each spin with a classical average dipolar field. Delicate issues raised in this deriv ation, like the neglect of quantum correlations between spins on diffe rent molecules at (repeated) initial times, are discussed with the hel p of exact calculations (for all spin temperatures) performed on a sim plified model which includes equal couplings between all N spins of a system. The same model is used to compare the merits of different form s of ''high temperature'' approximation. We also propose an iterative scheme for solving the ''modified Bloch-Redfield equations,'' in which the starting point is the well understood solution of the problem wit hout dipolar field. Finally, a short discussion is given of the relati on between ''quantum correlations'' and ''quantum coherences'' in the perspective of multiple-pulse and multiple-quantum experiments. These two notions are very simply related in the strict first approximation of weak order, and have often not been clearly distinguished. However, in the second order approximation, which is required whenever dipolar field effects manifest themselves, unrelated spins may display observ able coherences although they are not coupled (hence not correlated). (C) 1995 American Institute of Physics.