Superconductivity in magnesium diboride, MgB2, is described within the framework of Bogoliubov-Valatin two-band and two-gap formalism, employing a three-square-well potential model. The expressions for the superconducting transition temperature, T-c, and the isotope exponent, beta, are derived. Numerical calculations with the expressions newly reproduce near-experimental T-c (=38.50 K) and beta (=0.38). The influences of the interband attractive electron-acoustic (lambda(pi sigma)) and electron-optical (k(pi sigma)) phonons as well as repulsive Coulomb pseudopotential (mu(pi sigma)*) on T-c and beta are sketched. It is concluded that lambda(pi sigma) and k(pi sigma) have near-identical elevating effects on T-c and beta but mu(pi sigma)* has reverse effects, similar to the effect of interband impurity scattering.
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