Nuclear relaxation via paramagnetic impurities

In the first part of this study, the kinetics of nuclear relaxation via paramagnetic impurities for systems of arbitrary space dimension d (including fractal ones) is calculated under the assumptions that are commonly adopted at present for three-dimensional objects. In the second part, a new mean-field-type theory is formulated that reproduces all the results of the first part for integral values of d and which is intended for describing the process at longer times, when the kinetics calculated in the first part is not correct and when a crossover to Balagurov-Vaks asymptotic behavior begins to develop. Solutions to the equations of the new theory are constructed at integral values of d. In order to obtain these solutions, a method is developed for calculating the low-energy and long-wave asymptotic behavior of the off-shell T matrix for potential scattering in the case of singular repulsive potentials.