some considerations on the newly discovered superconducAnother measurable quantity which could unveil signativity at Tc = 39 in MgB2 [7]. This material has a structure tures of nonadiabaticity is the normal state Pauli suscepsimilar to that of GICs with the boron atoms forming tibility. As pointed out some time ago by Fay and layers of twodimensional honeycomb lattices. However, Appel [17], the lowest order electronphonon correction contrary to the GICs, the Fermi level crosses the inplane to is a vertex diagram, so that the renormalization of bands leading to a markedly twodimensional character the Pauli susceptibility is of order P = ph/EF. In the of the electronic properties. Moreover, the charge transfer adiabatic regime, therefore, is expected to be unaffected of the intercalated Mg atoms is such that the bands are by the electronphonon interaction. Conversely, when P is no longer negligible, acquires a dependence on and ph slightly doped with holes and the distance of the Fermi level crossing from the top of the band is only about 0.5 eV [20]. which could be detected by suitable experiments. We have This feature, together with the high phonon frequency of calculated the nonadiabatic effects on the Pauli susceptibility the boron atoms (ph up to 0.1 eV) indicates that MgBfor different stages of a perturbation theory in P and the could be in the nonadiabatic regime of the electronphonon results are shown in Fig. 3 [18]. In the figure, the dashed interaction. An additional interesting point is that MgB2 is lines refer to a simple ladder vertex correction while the solid far away fromhalffilling and in this case it has been shown lines are the results obtained by including the second order that the vertex corrections are mainly positive leading to nonadiabatic terms for different values of the momentum an amplified pairing even in the absence of strong electron cutoff Qc = qc/2kF. For P 0, both approximation correlations [21]. Further analysis of the relevance of this schemes reduce to the ME results = 0 = 2µBN0, where hypothesis is currently under development. µB is the Bohr magneton and N0 is the density of states at the Fermi level. The first main result (Fig. 3, a) is that in References the nonadiabatic regime (P = 0) is sensibly reduced with respect to the adiabatic limit 0. Hence, is no longer simply [1] A.B. Migdal. Sov. Phys. JETP 7, 996 (1958). proportional to N0. This means that disregarding the electon[2] G.M. Eliashberg. Sov. 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