  In a well-established many-body framework, successful in modeling a great
variety of nuclear processes, we analyze the role of the spectral functions
(SFs) accounting for the modifications of the dispersion relation of nucleons
embedded in a nuclear medium. We concentrate in processes mostly governed by
one-body mechanisms, and study possible approximations to evaluate the
particle-hole propagator using SFs. We also investigate how to include together
SFs and long-range RPA-correlation corrections in the evaluation of nuclear
response functions, discussing the existing interplay between both type of
nuclear effects. At low energy transfers (\le 50 MeV), we compare our
predictions for inclusive muon and radiative pion captures in nuclei, and
charge-current (CC) neutrino-nucleus cross sections with experimental results.
We also present an analysis of intermediate energy quasi-elastic neutrino
scattering for various targets and both neutrino and antineutrino CC driven
processes. In all cases, we pay special attention to estimate the uncertainties
affecting the theoretical predictions. In particular, we show that errors on
the \sigma_{\mu}/\sigma_e ratio are much smaller than 5%, and also much smaller
than the size of the SF+RPA nuclear corrections, which produce significant
effects, not only in the individual cross sections, but also in their ratio for
neutrino energies below 400 MeV. These latter nuclear corrections, beyond Pauli
blocking, turn out to be thus essential to achieve a correct theoretical
understanding of this ratio of cross sections of interest for appearance
neutrino oscillation experiments. We also briefly compare our SF and RPA
results to predictions obtained within other representative approaches.
