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 the accompanying paper for many-spin systems is applied here for calculating magnetic resonance signals of a spin A interacting with a bath of N identical spins B. Spins B are assumed to have much smaller gyromagnetic ratios than the spin A ~e.g., the former are nuclear spins, I and the latter is an electron spin, S!. The experimentally observed quadratic dependence of the spin-echo envelope decay on concentration and time is explained from considering 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 the rigid limit is due to the interaction of the A spin with the coherent many-body states of the coupled spins B via the nuclear flip-flop terms I6I7 , which becomes a dissipative mechanism in the thermodynamic limit. This represents a more rigorous analysis than simplified models based on an incoherent version of ‘‘spin diffusion,’’ and it leads to good quantitative agreement with experiment. Moreover, this analysis represents a unified description of both the modulation and decay of the A-spin echoes. Spin echoes and line shapes for the A – BN systems are also calculated for finite motions which randomize the B spins. Even for very slow motions ~modeled as translational diffusion! an effective mechanism for spin-echo envelope decay is generated, which readily overtakes the coherent mechanism in importance. The intensity distribution for the forbidden components in the A-spin line shape resulting from multiquantum transitions of the B spins caused by the pseudosecular interaction terms SzI6 , is calculated. In the rigid limit it is found to behave like a Poisson distribution. © 2001 American Institute of Physics. @DOI: 10.1063/1.1382817#