Electron Spectra in the Ionization of Atoms by Neutrinos

For neutrinos of O(10keV) energies, their oscillation lengths are less than a few hundred meters, thereby suggesting the fascinating idea of oscillation experiments of small geometrical size. To help evaluating this idea we calculate the ionization cross sections of H, He, Ne and Xe, using any neutrino flavor, in the few keV energy range. We find that the atomic ionization cross sections per electron are always smaller than the neutrino cross sections off free electrons, approaching it from below as the energy increases to the 100 keV region. At the 10-20 keV range though, atomic binding effects are very important, particularly for the heavier atoms, inducing a factor of two reduction of the Xe ionization cross section, compared to the free electron one.