  We study both the elastic ($\nu e \rightarrow \nu e$) and the radiative
process ($\nu e \rightarrow \nu e \gamma$) and discuss how these processes can
shed light on some current topics in neutrino physics such as a neutrino
magnetic moment and neutrino oscillations. The radiative process allows to
reach low values of $Q^2$ without the need to operate at very small energies of
recoil electrons, a favourable scenario to search for a neutrino magnetic
moment. The elastic cross section contains a dynamical zero at $E_{\nu}=m/(4
sin^2\theta_{W})$ and forward electrons for the electron antineutrino channel,
which is reachable at reactor facilities and accessible after the convolution
with the antineutrino spectrum. The implication for lepton flavour changing
transitions in that energy region searched for in neutrino oscillation
experiments, which combine disappearance and appearance rates, is discussed.
