Electron and neutrino scattering from the QE to the DIS region

I will present our latest results for lepton-nucleus scattering cross sections obtained within nuclear many-body approaches relying on accurate models of nuclear dynamics. The Green’s Function Monte Carlo approach allows to provide virtually-exact electroweak responses of nuclei up to A=12. I will present electron - 4He cross sections for a variety of kinematical setups, with a focus on relativistic correction in the kinematics, and show preliminary results for the electroweak charged-current 4He responses. Then, I will outline the formalism based on the impulse approximation and spectral function. In particular, I will present the results we obtained for charged-and neutral-current transitions in neutrino scattering processes off 12C and 16O using two different models of the nuclear spectral function. The role played by relativistic two-body electroweak current operators and the pion-production mechanisms, included for the first time in our calculations, will be also discussed in detail.