  In small Fermi energy metals, disorder can deeply modify superconducting
state properties leading to a strong suppression of the critical temperature
$T_c$. In this paper, we show that also normal state properties can be
seriously influenced by disorder when the Fermi energy $E_{\rm F}$ is
sufficiently small. We calculate the normal state spin susceptibility $\chi$
for a narrow band electron-phonon coupled metal as a function of the
non-magnetic impurity scattering rate $\gamma_{\rm imp}$. We find that as soon
as $\gamma_{\rm imp}$ is comparable to $E_{\rm F}$, $\chi$ is strongly reduced
with respect to its value in the clean limit. The effects of the
electron-phonon interaction including the nonadiabatic corrections are
discussed. Our results strongly suggest that the recent finding on irradiated
MgB$_2$ samples can be naturally explained in terms of small $E_{\rm F}$ values
associated with the $\sigma$-bands of the boron plane, sustaining therefore the
hypothesis that MgB$_2$ is a nonadiabatic metal.
