Irreversibility in Paramagnetic Spin Systems: Free Induction Decay and Spin Diffusion

In a recent work, the authors derived kinetic equations for the spin autocorrelation function for a paramagnetic spin system using the resummation procedure introduced by Résibois and De Leener in the framework of the statistical mechanics of irreversible processes due to Prigogine and co-workers. These equations are non-Markovian and nonlinear in the high-field, high-temperature, and Weiss-limit approximations. In the present paper, methods of approximation are given to solve such kinetic equations and are applied to the study of two important NMR problems, namely, free induction decay (FID) and spin diffusion. The general characteristics of the FID are obtained even in the lowest order of approximation owing to the resummation procedure, whereas the next higher-order correction leads to very good agreement with the experimental results given by Barnaal and Lowe. The following asymptotic form is also derived: $\Gamma \mathrm{}\left(t\right)=(acos\alpha t+bsin\alpha t)e^{-\beta t}$ A diffusion equation is obtained for the magnetization. From this the diffusion coefficient is computed and is found to be in agreement with that proposed by several authors. However, consideration of higher-order corrections does not seem to explain the strong dependence on the orientation of the external magnetic field which was observed experimentally by Leppelmeier.