Pauli susceptibility of nonadiabatic Fermi liquids

The nonadiabatic regime of the electron-phonon interaction leads to behavio rs of some physical measurable quantities qualitatively different from thos e expected from the Migdal-Eliashberg theory. Here we identify in the Pauli paramagnetic susceptibility chi one of such quantities and show that the n onadiabatic corrections reduce chi with respect to its adiabatic limit. We also show that the nonadiabatic regime induces an isotope dependence of chi , which in principle could be measured.