Large perturbations and nonexponential decays in spin relaxation. Applications of the memory function theory

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Abstract
Our memory function theory of time correlation functions [J. Chem. Phys. 62, 2098 (1975)] is applied to two problems which are met in the theory of protonrelaxation in aqueous solutions of Ni++. In this system the modulation of the zero‐field splitting (zfs) which drives the electron spin relaxation is neither small enough nor fast enough for the usual second‐order perturbation calculation to be accurate or for the relaxation to obey Bloch’s equations. Here the perturbation series for the memory function is rearranged to give a new series which converges rapidly even when the perturbation is large. This result is exact for a particular model for the modulation process and for vanishing external magnetic field. It is applicable as an approximation method more generally. When the Solomon–Bloembergen equations are used to calculate the relaxation rates of the protons due to interaction with the electron spins, and the latter do not obey Bloch’s equations, then we show how the electron spin relaxation times and Larmor frequency are to be replaced by ’’effective’’ parameters which now depend upon the modulation of the proton–electron spin interaction as well as on the field and the parameters of the zfs interaction. Finally, calculations for protonrelaxation rates based on the new theory are compared with those done in a standard way for the case of interest.