  We study the question of whether coherent neutrino scattering can occur on
macroscopic scales, leading to a significant increase of the detection cross
section. We concentrate on radiative neutrino scattering on atomic electrons
(or on free electrons in a conductor). Such processes can be coherent provided
that the net electron recoil momentum, i.e. the momentum transfer from the
neutrino minus the momentum of the emitted photon, is sufficiently small. The
radiative processes is an attractive possibility as the energy of the emitted
photons can be as large as the momentum transfer to the electron system and
therefore the problem of detecting extremely low energy recoils can be avoided.
The requirement of macroscopic coherence severely constrains the phase space
available for the scattered particle and the emitted photon. We show that in
the case of the scattering mediated by the usual weak neutral current and
charged current interactions this leads to a strong suppression of the
elementary cross sections and therefore the requirement of macroscopic
coherence results in a reduction rather than an increase of the total detection
cross section. However, for the $\nu e$ scattering mediated by neutrino
magnetic or electric dipole moments coherence effects can actually increase the
detection rates. Effects of macroscopic coherence can also allow detection of
neutrinos in 100 eV -- a few keV energy range, which is currently not
accessible to the experiment. A similar coherent enhancement mechanism can work
for relativistic particles in the dark sector, but not for the conventionally
considered non-relativistic dark matter.
