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Strange quark contributions to the neutral current reaction in the neutrinoscattering are investigated on the nucleon level and extended to the $^{12}$Ctarget nucleus through the neutrino-induced knocked-out nucleon process in thequasi-elastic region within the framework of a relativistic single particlemodel. The incident energy range between 500 MeV and 1.0 GeV is used for theneutrino(antineutrino) scattering. Effects of the final state interaction forthe knocked-out nucleon are included by a relativistic optical potential. Wefound that the sensitivity of the strange quark contents could be salient onthe asymmetry between neutrino and antineutrino scattering cross sections. Inspecific, $A (\nu ({\bar \nu}), \nu^{'} ({\bar \nu}^{'}) N)$ reaction is shownto be very sensitive test in the searches of the strangeness.

Strange quark contributions to neutrino and antineutrino nucleus scattering via neutral current in quasi-elastic region