The determination of the electron-phonon interaction from tunneling data in the two-band superconductor MgB2

We calculate the tunneling density of states (DOS) of MgB2 for different tunneling directions, by directly solving the real-axis, two-band Eliashberg equations (EE). Then we show that the numeric inversion of the standard single-band EE, if applied to the DOS of the two-band superconductor MgB2, may lead to wrong estimates of the strength of certain phonon branches (e.g. the E_2g) in the extracted electron-phonon spectral function alpha^(2)F(omega). The fine structures produced by the two-band interaction turn out to be clearly observable only for tunneling along the ab planes in high-quality single crystals. The results are compared to recent experimental data.