Magnetic spin lattice relaxation in the presence of spin-diffusion

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Abstract
The equations describing the spin-diffusion-coupled nuclear magnetic spin-lattice relaxation behaviour of a one-dimensional, two-region system are solved exactly. The solutions allow the calculation of the relaxation times and their associated amplitudes in terms of the values of the sizes, spin-diffusion coefficients and intrinsic relaxation times of each region. The morphology of the roots of the equation are represented graphically in a manner which illustrates their behaviour as a function of the system parameters. The results obtained from these exact calculations are compared with numerically simulated data which mimic experimental measurements and which are fitted to a maximum of four exponential processes. Good agreement is demonstrated, particularly for the longer relaxation components when there are several roots with significant amplitude. Preliminary consideration is given to the inverse problem of deriving system parameters from the observed relaxation behaviour.