The dependence of the critical current density, J c , on the gamma irradiation dose in MgB 2 polycrystalline superconducting specimens has been studied. The MgB 2 samples were irradiated with 10 MR and 20 MR doses of γ-rays. The critical current density, J c was found to be enhanced almost at all temperatures after irradiation. The enhancement of J c was found to be linear with the irradiation dose at all temperatures. We also report on the correlation between the superconducting transition temperature and the residual resistivity ratio. Most of our results agree with the Testardi and Mooij rules which suggest that the dominant pairing mechanism of MgB 2 is the phonon-mediated interaction.