Inclusive charged-current neutrino-nucleus scattering in the quasielastic region

Abstract

We study inclusive charged-current reaction through total cross sections of neutrino-nucleus scattering within the framework of a relativistic single-particle model in the quasielastic region. To describe the final-state interaction between knocked-out nucleons and the residual nucleus, a real potential of final nucleons, which is generated by a relativistic mean field, is used with the assumption of no loss of flux, which leads to current conservation and gauge invariance. We calculate $({\ensuremath{\nu}}_{\ensuremath{\mu}},{\ensuremath{\mu}}^{\ensuremath{-}})$ and $({\mathrm{\ensuremath{\nu}\ifmmode \bar{}\else \={}\fi{}}}_{\ensuremath{\mu}},{\ensuremath{\mu}}^{+})$ reactions. In these calculations, $^{12}\mathrm{C}$, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ are used as target nuclei and the incident neutrino (antineutrino) energies are exploited up to 4 GeV. We find that the effect of the final-state interaction by the real potential of the knocked-out nucleons reduces cross sections by about 15%, similar to the effect of electron scattering. Furthermore, the effect of the Coulomb distortion for the outgoing leptons is shown to be different from the electron scattering. Finally, our total cross sections by scaling number of participated nucleons are presented to compare with experimental data.