Neutrino-impact ionization of atoms in searches for neutrino magnetic moment

The ionization of atomic electrons by scattering of neutrinos is revisited. This process is the one studied in the experimental searches for a neutrino magnetic moment using germanium detectors. Current experiments are sensitive to the ionization energy comparable with the atomic energies, and the effects of the electron binding should be taken into account. We find that the so-called stepping approximation to the neutrino-impact ionization is in fact exact in the semiclassical limit and also that the deviations from this approximation are very small already for the lowest bound Coulomb states. We also consider the effects of electron-electron correlations and argue that the resulting corrections to the ionization of independent electrons are quite small. In particular we estimate that in germanium these are at a one percent level at the energy transfer down to a fraction of keV. Exact sum rules are also presented as well as analytical results for a few lowest hydrogen-like states.