  Background: Neutrinos in the low-energy regime provide a gateway to a wealth
of interesting physics. While plenty of literature exists on detailing the
calculation and measurement of total reaction strengths, relatively little
attention is paid to the measurement and modeling of the final lepton through
differential cross sections at low energies, despite the experimental
importance.
  Purpose: We calculate differential cross sections for low-energy
neutrino-nucleus scattering. We examine the role played by forbidden
transitions in these distributions and how this differs across different
energies and nuclear target masses. Attention is also paid to predictions for
typical experimental neutrino spectra.
  Method: The differential cross sections are calculated within a Continuum
Random Phase Approximation framework, which allows us to include collective
excitations induced by long-range correlations. The Coulomb interaction of the
final lepton in charged current events is treated in an effective way.
  Results: Kinematic distributions are calculated for $^{16}$O, $^{40}$Ar and
$^{208}$Pb. $^{40}$Ar model results are compared for CC ($\nu_e,e^-$) reactions
to events generated by the MARLEY event generator, with noticeable
discrepancies.
  Conclusion: Forbidden transitions have a marked effect on the kinematic
distributions of the final lepton at low-energy kinematics, such as for DAR
neutrinos or for a Fermi-Dirac spectrum at low temperature. This could
introduce biases in experimental analyses. Backwards scattering is noticeably
more prominent than with MARLEY.
