Nuclear models for inclusive lepton-nucleus scattering in the quasi-elastic region and beyond

High-precision measurements in neutrino oscillation experiments require a very accurate description of the lepton-nucleus scattering process. Several cross-section calculations are available, but important discrepancies are still present between different model predictions. For the quasi-elastic channel, dominated by one particle-one hole excitations, an overview over several nuclear models - specifically Relativistic Fermi Gas, SuperScaling Approach, Spectral Function, Hartree-Fock and Random Phase Approximation - is presented and compared with data for electron-nucleus scattering, a very important process for testing theoretical models validity, highlighting the specific features of each approach. Furthermore an ongoing microscopic calculation of the two particle-two hole excitations contribution to the electromagnetic response is presented, and some preliminary results are shown.