We present a detailed theoretical and experimental NQR multiple-pulse spin-locking study of spin-lattice relaxation and spin diffusion processes in the presence of paramagnetic impurities in solids. The relaxation function of the nuclear spin system at the beginning of the relaxation process is given by exp (-t/T1rho)alpha, where T1rho is spin-lattice relaxation time in rotating frame and alpha = d/6, d is the sample dimensionality. Then the relaxation proceeds asymptotically to an exponential function of time, which was attributed to the spin-diffusion regime. Using the experimental data obtained from the analysis of those two relaxation regimes in gamma-irradiated powdered NaClO3, spin diffusion coefficient has been determined and the radius of the diffusion barrier has been estimated.