  A substantial fraction of systematic uncertainties in neutrino oscillation
experiments stems from the lack of precision in modeling the nucleus when
describing the neutrino-nucleus interactions. The Spectral Function (SF) model
features a distribution of momenta and removal energies of nucleons inside the
nucleus within the shell-model picture, and also accounts for short-range
correlations between nucleons. These characteristics offer significant
improvements with respect to the more commonly used Fermi gas-based models.
Electron scattering experiments offer a precise probe of the structure of the
nucleus and have been used to both construct and validate the SF model. SF is
thus an interesting reference model for long baseline neutrino experiments.
  Based on constraints from electron scattering data, we develop a set of
parameters that can alter the occupancy of the nuclear shells and the
distribution of the nucleon momentum within each shell. In addition, the impact
of final-state interactions on the outgoing lepton and nucleon kinematics, the
contribution of short-range correlations and the effect of Pauli blocking can
also be modified. In this document, we will first describe the development of
these parameters, partially based on a comparison with electron scattering
data. We then show fits of these parameters to available T2K and MINER$\nu$A
cross-section data and discuss how they can be used to constrain the systematic
uncertainties related to the SF model in neutrino oscillation analyses.
