Nuclear Magnetic Relaxation in the Presence of Paramagnetic Ions

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Abstract
The influence of independent processes of relaxation of paramagnetic ions on nuclear magnetic relaxation in the presence of these ions is discussed theoretically, using the Kubo and Tomita method. The nuclei are assumed to relax as a result of their contact with the ions through the usual dipole-dipole mechanism and this interaction is, in turn, considered to be of negligible influence on the ionic relaxation. Following a suggestion by Abragam, the ionic interactions are described as a coupling of the ionic spins to an effective local field varying randomly in time; this coupling is finally expressed in terms of experimentally more accessible parameters such as the ionic correlation and relaxation times. All dissipative interactions are approximated by autocorrelation functions with simple exponentially decaying time dependence, thereby limiting the applicability of this calculation to liquids and to liquid-like solids. The second-order terms in the perturbation expansion of the relaxation tensor yield contributions to the Bloch relaxation times of the system of nuclear spins that agree with previous calculations by Solomon. The fourth-order terms describing ionic relaxation yield a contribution to the nuclear relaxation times with a narrowing influence, except in the limit of very strong fields when a broadening is produced.