Effects of density-dependent weak form factors on charged-current neutrino-nucleus scattering in the quasi-elastic region

Abstract

We study the effects of density-dependent electromagnetic, axial, and weak vector form factors on the inclusive $(e,{e}^{\ensuremath{'}})$ reaction and the charged-current neutrino-nucleus scattering in the quasi-elastic region within the framework of a relativistic single-particle model. The density-dependent form factors obtained from a quark-meson coupling model are applied into the $(e,{e}^{\ensuremath{'}})$ reaction and the neutrino-nucleus scattering via charged current. The effects of the density-dependent form factors increase the $(e,{e}^{\ensuremath{'}})$ cross sections by a few percent. However, the effects may reduce the differential cross sections up to 20% (60%) at $\ensuremath{\rho}=1.0{\ensuremath{\rho}}_{0}\phantom{\rule{4pt}{0ex}}(2.0{\ensuremath{\rho}}_{0})$ for the antineutrino scattering and also reduce the cross section up to 20% (30%) at $\ensuremath{\rho}=1.0{\ensuremath{\rho}}_{0}\phantom{\rule{4pt}{0ex}}(2.0{\ensuremath{\rho}}_{0})$ for the neutrino scattering around the peak positions, where the normal density is ${\ensuremath{\rho}}_{0}\ensuremath{\sim}0.15$ ${\mathrm{fm}}^{\ensuremath{-}3}$. For the density of finite nuclei such as $^{12}\mathrm{C}$, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ as 0.6, 0.7, and 1.0 of ${\ensuremath{\rho}}_{0}$, the in-medium effects are 20% to 30%, even in the antineutrino case. Our theoretical double-differential and total cross sections are compared with the recent MiniBooNE data for $^{12}\mathrm{C}({\ensuremath{\nu}}_{\ensuremath{\mu}},{\ensuremath{\mu}}^{\ensuremath{-}})$ scattering.