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Pressure dependence of critical temperature in MgB2 and two bands Eliashberg theory

The variation of the superconducting critical temperature Tc as a function of the pressure p in the magnesium diboride MgB2 has been studied in the framework of two-bands Eliashberg theory and traditional phonon coupling mechanism. I have solved the two-bands Eliashberg equations using first-principle calculations or simple assumptions for the variation, with the pressure, of the relevant physical quantities. I have found that the experimental Tc versus p curve can be fitted very well and information can be obtained on the dependence of the electron-phonon interaction matrix <I^{2}> by pressure. The pressure dependence of the superconductive gaps Delta{sigma} and Delta{pi} is also predicted.