A many-body analysis of the effects of the matrix protons and their diffusional motion on electron spin resonance line shapes and electron spin echoes

The method for treating the evolution of the density matrix developed in th e accompanying paper for many-spin systems is applied here for calculating magnetic resonance signals of a spin A interacting with a bath of N identic al spins B. Spins B are assumed to have much smaller gyromagnetic ratios th an the spin A (e.g., the former are nuclear spins, I and the latter is an e lectron spin, S). The experimentally observed quadratic dependence of the s pin-echo envelope decay on concentration and time is explained from conside ring the dipolar coupling of spin A to all the B spins in the presence of B -B dipolar interactions. It is shown that the spin-echo envelope decay in t he rigid limit is due to the interaction of the A spin with the coherent ma ny-body states of the coupled spins B via the nuclear flip-flop terms I+/-I -/+ which becomes a dissipative mechanism in the thermodynamic limit. This represents a more rigorous analysis than simplified models based on an inco herent version of "spin diffusion," and it leads to good quantitative agree ment with experiment. Moreover, this analysis represents a unified descript ion of both the modulation and decay of the A-spin echoes. Spin echoes and line shapes for the A-B-N systems are also calculated for finite motions wh ich randomize the B spins. Even for very slow motions (modeled as translati onal diffusion) an effective mechanism for spin-echo envelope decay is gene rated, which readily overtakes the coherent mechanism in importance. The in tensity distribution for the forbidden components in the A-spin line shape resulting from multiquantum transitions of the B spins caused by the pseudo secular interaction terms SzI+/-, is calculated. In the rigid limit it is f ound to behave like a Poisson distribution. (C) 2001 American Institute of Physics.