Dipolar relaxation in a many-body system of spins of 1/2

The method utilized in Paper I [J. Chem. Phys. 112, 1413 (2000)] for treati ng the density matrix equation for a two-spin system in the presence of the dipolar interaction that is randomly modulated by translational diffusion, is extended to a many-body system of identical spins of 1/2. Generalized c umulant expansions are used, which allow one to take full advantage of the statistical independence of the motions of spins. In the high-temperature a pproximation (appropriate for dilute solutions), for a single nonselective pulse, the symmetry of the problem allows one to obtain a compact ordered b inomial expression for the free-induction decay signal that is related to t he two-particle solution, and it still contains the two spin-isochromat com ponents. The latter are evaluated by solving the corresponding stochastic L iouville equation, which allows one to recover in a unified way the two lim iting cases including Anderson's result for statistical broadening in a rig id lattice and the classical Torrey-Bloembergen-Redfield expression for the motional narrowing, as corrected by Hwang and Freed. The line shape expres sion in the thermodynamic limit, i.e., for large numbers of particles in a macroscopic volume, is obtained. It is found that the many-body dipolar lin e shapes are very close to Lorentzians over the entire motional range studi ed, with the linewidths proportional to the spin concentration, as predicte d earlier for the limiting cases. Linewidths plotted versus the values of t he translational diffusion coefficient clearly show the solid-state limit, the motional-narrowing limit, and the intermediate region. The method is ex tended to describe the behavior of the many-body system in a solid-echo seq uence. This enables one to obtain the homogeneous T-2's over the whole rang e of motions. A minimum in T-2 is found at approximately the same value of translational diffusion coefficient as was found for the two-spin case in P aper I. (C) 2000 American Institute of Physics. [S0021-9606(00)02903-2].