The free energy of a 2-band superconductor was obtained by taking into account all actual electron–phonon and Coulomb interactions. The temperature dependences of the superconducting gaps, the specific heat with its jump at TC were calculated by minimizing the free energy. The theory was applied to the MgB2 superconductor. The TC isotope effect was estimated and agreement with experiment was obtained.

A Generalized Two-Band Model for the Superconductivity in MgB2. P.Konsin, B.Sorkin: Superconductor Science and Technology, 2004, 17, 1472-6