  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.
