On the rate of Tc suppression by the interband impurity scattering in MgB2

We calculate the change in the superconducting transition temperature Tc of MgB2 caused by interband nonmagnetic impurity scattering using the Eliashberg theory for the two-band model of this compound. Much slower rate of Tc suppression is obtained compared to the prediction based on the BCS treatment of the two-band model which ignores renormalization and damping associated with the electron-phonon interaction. Hence, the interband impurity scattering rates deduced from experiments on MgB2 using the formula which results from the BCS approach to the two-band model are underestimated. We generalize the BCS treatment of the two-band model to include renormalization effects of the electron-phonon interaction and find an excellent agreement with the full strong coupling calculation.