We studied the effect of disorder on the superconducting properties of polycrystalline MgB_2 by specific-heat measurements. In the pristine state, these measurements give a bulk confirmation of the presence of two superconducting gaps with 2 Delta 0 / k_B T_c = 1.3 and 3.9 with nearly equal weights. The scattering introduced by irradiation suppresses T_c and tends to average the two gaps although less than predicted by theory. We also found that by a suitable irradiation process by fast neutrons, a substantial bulk increase of dH_{c2}/dT at T_c can be obtained without sacrificing more than a few degrees in T_c. The upper critical field of the sample after irradiation exceeds 28 T at T goes to 0 K.
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