H atoms produced by the gamma -ray irradiation of solid para-H-2 (p-H-2) and solid normal-H-2 (n-H-2) decay gradually when the irradiated sample is stored at 4.2 K. ortho-H-2 (o-H-2) molecules at the sites nearest an H atom in solid n-H-2 convert to p-H-2 molecules by interacting with the H atom. H atoms in solid H-2 decay by the process of tunneling diffusion H + p-H-2 --> p-H-2 + H and finally recombine with other I-I atoms. The rate constants for the tunneling reaction were obtained from the decay rates of H atoms in solid H-2 at various concentrations of o-H-2 When solid n-H-2 is stored for 10 h at 4.2 K after gamma -ray irradiation, a number of o-H-2 molecules change into p-H-2 molecules by a catalytic chain reaction induced by mobile H atoms. The G value of the o-H-2 yields from H atoms amounts to 1-2.6 x 10(4). The rate constant for the tunneling reaction ii + p-H-2 --> p-H-2 + H decreases drastically with increasing numbers of o-H-2 molecules, which exist as orientational defects in solid p-H-2. It was concluded that a very small amount of energy (ca. 2 cal mol(-1)) affects the tunneling reaction at very low temperatures.