Approximate treatment of lepton distortion in charged-current neutrino scattering from nuclei

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" approximation seems to work so well that for muons the full distorted-wave treatment is usually unnecessary, even at kinetic energies as low as 1 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 often proves perfectly adequate. Scattering of electron neutrinos from muon decay on iodine and of atmospheric neutrinos on iron is discussed in light of these results.