Constraints on the mechanism of superconductivity for MgB2 from Tc and the total isotope effect

We examine the possible electron-phonon spectra that produce both T_c=39 K and an isotope coefficient β=0.32±0.01, with Eliashberg theory. We assess the viability of the conventional electron-phonon mechanism in light of these results, compared with ab initio calculations of the electron-phonon spectrum. Comparisons are made with similar considerations for low T_c materials.