Effects of the density-dependent weak form factors on the neutrino reaction via neutral current for the nucleon in nuclear medium and ${}^{12}$C

Abstract

The nucleon form factors in free space are usually thought to be modified when a nucleon is bound in a nucleus or immersed in a nuclear medium. We investigate effects of the density-dependent axial and weak-vector form factors on the electro-neutrino (${\nu }_e$) and anti-electro-neutrino $({\bar{\nu }}_e)$ reactions via neutral current (NC) for a nucleon in nuclear medium or ${}^{12}$C. For the density-dependent form factors, we exploit the quark-meson-coupling (QMC) model, and apply them to the ${\nu }_e$ and ${\bar{\nu }}_e$ induced reactions by NC. About 12% decrease of the total cross section by ${\nu }_e$ reaction on the nucleon is obtained at normal density, $\rho ={\rho }_0\sim 0.15{fm}^{-3}$, as well as about 18% reduction of total ${\nu }_e$ cross section on ${}^{12}$C, by the modification of the weak form factors of the bound nucleon. However, similarly to the charged current reaction, effects of the nucleon property change in the ${\bar{\nu }}_e$ reaction reduce significantly the cross sections about 30% for the nucleon in matter and ${}^{12}$C cases. Such a large asymmetry in the ${\bar{\nu }}_e$ cross sections is addressed to originate from the different helicities of ${\bar{\nu }}_e$ and ${\nu }_e$.