  The reconstruction of the neutrino energy is crucial in oscillation
experiments that use interactions with nuclei to detect the neutrino.
  The common reconstruction procedure is based on the kinematics of the
final-state lepton. The interpretation of the reconstructed energy in terms of
the real neutrino energy must rely on a model for the neutrino-nucleus
interaction. The Relativistic Fermi Gas (RFG) model is frequently used in these
analyses. In the Hartree-Fock (HF) model for quasielastic nucleon knockout, the
bound nucleon wave functions are obtained using an effective nucleon-nucleon
force. The final-state wave function is constructed from continuum states in
the same potential which have the correct asymptotic behavior. The Continuum
Random Phase Approximation (CRPA) model extends the HF approach taking long
range correlations into account in a self-consistent way. Considering only
single-nucleon processes, the distributions of reconstructed neutrino energies
obtained within the HF-CRPA approach are compared with the results of the RFG,
an RPWIA calculation, and the RPA+np-nh model of Martini et al.
  We find that the distributions of reconstructed energies for a fixed incoming
energy in the HF-CRPA display additional strength in the low reconstructed
energy tails compared to models without elastic distortion of the outgoing
nucleon. This asymmetry redistributes strength from higher to lower values of
the reconstructed energy. The mean field description of the nuclear dynamics
results in a reshaping of the reconstructed energy distribution that cannot be
accounted for in a plane wave impulse approximation model, even by modifying ad
hoc parameters such as the binding energy. In particular it is shown that in
the RFG calculations there is no value of the binding energy which is able to
reproduce the entire T2K $\nu_\mu$ oscillated spectrum as calculated in
HF-CRPA.
