Approximate Treatment of Lepton Distortion in Charged-Current Neutrino Scattering from Nuclei

Abstract

The partial-wave expansion used to treat the distortion of scattered electrons by the nuclear Coulomb field is simpler and considerably less time-consuming when applied to the production of muons and electrons by low and intermediate-energy neutrinos. For angle-integrated cross sections, however, a modification of the "effective-momentum-transfer" approximation seems to work so well that for muons the full distorted-wave treatment is usually unnecessary, even at kinetic energies as low as an MeV and in nuclei as heavy as lead. The method does not work as well for electron production at low energies, but there a Fermi function usually proves adequate. Scattering of electron-neutrinos from muon decay on iodine and of atmospheric neutrinos on iron are discussed in light of these results.