  We show the existence of dynamical zeros in the helicity amplitudes for
neutrino-electron elastic scattering at lowest order in the standard theory. In
particular, the $\lambda=1/2$ non-flip electron helicity amplitude in the
electron antineutrino process vanishes for an incident neutrino energy
$E_{\nu}=m_{e}/(4sin^{2}\theta_{W})$ and forward electrons (maximum recoil
energy). The rest of helicity amplitudes show kinematical zeros in this
configuration and therefore the cross section vanishes. Prospects to search for
neutrino magnetic moment are discussed.
