Strange quark contributions to the neutrino (antineutrino) scattering are investigated on the elastic neutrino-nucleon scattering and the neutrino-nucleus scattering for 12C target in the quasi-elastic region on the incident energy of 500 MeV, within the framework of a relativistic single particle model. For the neutrino-nucleus scattering, the effects of final state interaction for the knocked-out nucleon are included by a relativistic optical potential. In the cross sections we found some cancellations of the strange quark contributions between the knocked-out protons and neutrons. Consequently, the asymmetries between the incident neutrino and antineutrino which is the ratio of neutral current to charged current, and the difference between the asymmetries are shown to be able to yield more feasible quantities for the strangeness effects. In order to explicitly display importance of the cancellations, results of the exclusive reaction 16O( u, u p) are additionally presented for detecting the strangeness effects.
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