Abstract
We present the neutral- and charged-current reactions by incident neutrino (antineutrino) scattering on the nucleon and on the $^{12}\mathrm{C}$ target in the quasi-elastic region within the framework of a relativistic single-particle model. The incident energies at 500 MeV and 1 GeV are used for the scattering. Effects of strangeness are studied thoroughly on the cross sections, the ratios between the neutral- and charged-current reactions, and the asymmetries by incident neutrino and antineutrino. We find that there exists some cancellation of the strange quark contributions between the knocked-out protons and neutrons in the neutrino (antineutrino)-nucleus scattering. The effect of strangeness is exhibited more strongly on the asymmetry than on the ratio or cross section. On a difference of the asymmetry, the effect of strangeness appears strongly, but on a summation of the asymmetry, the effect almost disappears in the low and middle kinetic energies of the knocked-out nucleon.
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