Random distribution of paramagnetic centers in the nuclear spin-lattice relaxation

A numerical solution is presented for the differential equation governing the nuclear spin-lattice relaxation via paramagnetic centers for spherically symmetric spin-diffusion constantD and direct relaxation transition probabilityC in the one-paramagnetic-center approximation. An interpolation function is given which reproduces the computedT ₁ values within ±5% for both the rapid diffusion and diffusion-limited cases. The introduction of a random distribution of the paramagnetic centers over the sample causes the relaxation to occur as exp(?at ^h ) with 0.5<h<1.0 forβ=(C/D)^1/4<R _av=the average radius of the influence spheres. This differs from the experimentally observed exp(?a ₁ t) behaviour. However, the random distribution seems to explain the difference between the theoretically calculated fluorine spin-diffusion in CaF₂ and that extracted from experimental NMR data by using the uniform-distribution model.