Coherent scattering and macroscopic coherence: Implications for neutrino, dark matter and axion detection

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.