Nuclear spin-lattice relaxation via paramagnetic impurities in solids with arbitrary space dimension

We extend the theory of growth of the nuclear magnetization in the presence of paramagnetic impurities and the absence of spin diffusion to the case of solids with arbitrary space dimension D. We show that the rate of growth of the magnetization is proportional to exp(-Atα) where t is the time and α is a fractional power which depends on the concentration and distribution of the paramagnetic centers and the magnetic nuclei. In the homogeneous distribution, α=D/6. In the inhomogeneous distribution, the sample can be regarded as consisting of subsystems packed in the d-dimensional space of the sample, each of which includes a paramagnetic center surrounded by nuclei. This model results in the expression α=(D+d)/6. Experimental data are presented for both of these cases.