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

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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 (νₑ) and anti-electro-neutrino (νₑ) reactions via neutral current (NC) for a nucleon in nuclear medium or ¹²C. For the density-dependent form factors, we exploit the quark-meson-coupling (QMC) model, and apply them to the νₑ and νₑ induced reactions by NC. About 12% decrease of the total cross section by νₑ reaction on the nucleon is obtained at normal density, ρ= ρ₀ 0.15 fm⁻³, as well as about 18% reduction of total νₑ cross section on ¹²C, 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 νₑ reaction reduce significantly the cross sections about 30% for the nucleon in matter and ¹²C cases. Such a large asymmetry in the νₑ cross sections is addressed to originate from the different helicities of νₑ and νₑ.