A BPP (Bloembergen-Purcell-Pound) model for nuclear spin relaxation due to diffusion in disordered systems: combined barrier- and site-energy disorder

Nuclear spin relaxation rates due to magnetic interactions between diffusing spins in ordered systems are often interpreted in terms of an exponential correlation function (the BPP model). The common extension of this to disordered systems is to average the relaxation rate for a jump rate with energy E over a distribution N ( E ) of energies in the disordered system. A more rigorous extension of the BPP model to disordered systems is described which incorporates simultaneous barrier- and site-energy distributions. An efficient computational scheme is developed to evaluate the triple integrals required. Results are presented for the correlation functions and relaxation rates for some typical values of parameters for both of the above extensions of the BPP model to disordered systems. There are significant differences between the results for the two models. The model presented here provides a means of analysing experimental relaxation data to deduce information about both barrier- and site-energy distributions.