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 with incident energy E _ { \nu } \leq 80 MeV via neutral current ( NC ) for a nucleon in a 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 the \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 the 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 } .