  One of the most important predictions of the two-gap theory of
superconductivity concerns the role of interband scattering (IBS) by
impurities. IBS is expected to decrease the critical temperature, Tc, of MgB2
to a saturation value of about 20 K, where the two gaps merge to a single one.
These predictions have been partially contradicted by experiments. In fact, Tc
does not saturate in irradiated samples, but decreases linearly with residual
resistivity and the merging of the gaps has been observed at a much lower Tc
(11 K). In this paper we argue that, while at low level of disorder IBS is the
leading mechanism that suppresses superconductivity, at higher disorder the
experimental results can only be understood if the smearing of the density of
states due to intraband electron lifetime effects is considered.
