We report on the direct observation of stretched exponential relaxation in low-temperature monatomic Lennard-Jones systems which were cooled slowly from the liquid phase to form crystals with a large number of defects. We use the cage correlation function [E. Rabani, J. D. Gezelter, and B. J. Berne, J. Chem. Phys. 107, 6867 (1997)] which measures changes in atomic surroundings to observe the stretched exponential relaxations. We obtain a distribution of hopping rates assuming that the origin of the Kohlrausch-Williams-Watts law is from static disorder in the distribution of barrier heights

PACS numbers: 66.30.-h, 02.70.Ns, 31.15.Qg, 61.43.Er