Nuclear spin relaxation by translational diffusion in solids: X. Monte Carlo calculation for the simple hopping model

The spectral density functions J(p)( omega ) relevant to nuclear spin relaxation rates due to magnetic dipole coupling between diffusing spins in cubic crystals are calculated, for the simple hopping model, by a Monte Carlo method. The analysis makes use of known exact results in various limits. The statistical fluctuations in the Monte Carlo calculations become more significant at high frequencies but accurate analytic results are known in this regime. Numerical results are therefore obtained over the entire frequency range for all spin concentrations except the monovacancy limit.