For neutrinos of $\mathcal{O}(10\mathrm{k}\mathrm{e}\mathrm{V})$ 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 in evaluating this idea, a formalism is developed for calculating the neutrino ionization cross sections for H as well as the noble atoms. This formalism is based on the use of spin-independent atomic wave functions and should very accurately describe the ionization spectra for H, He, Ne, and Ar. The accuracy is considerably reduced for the Xe case though, where the spin dependence in the wave functions is non-negligible. Nevertheless, even for Xe the results remain qualitatively correct. In all cases, the atomic ionizations cross section per electron is found to be smaller than the neutrino cross section off free electrons, approaching it from below as the energy increases to the 100 keV region. At the 10–20 keV range though, the atomic binding effects in the cross sections and the spectra are very important and increasing with the atomic number. They are canceling out though, when total ionization cross section ratios, like ${\nu }_{\mu }/{\nu }_e$ or ${\overline{\nu }}_{\mu }/{\overline{\nu }}_e$, are considered.

• Received 9 September 2004

DOI:https://doi.org/10.1103/PhysRevD.70.113008