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Super-Kamiokande has reported the results for the lepton events in the atmospheric neutrino experiment. These results have been presented for a 22.5kT water fiducial mass on an exposure of 1489 days, and the events are divided into sub-GeV, multi-GeV and PC events. We have presented a study of nuclear medium effects in the sub-GeV energy region of atmospheric neutrino events for the quasielastic scattering, incoherent and coherent pion production processes, as they give the most dominant contribution to the lepton events in this energy region. We have used the atmospheric neutrino flux given by Honda et al. These calculations have been done in the local density approximation. We took into account the effect of Pauli blocking, Fermi motion, Coulomb effect, renormalization of weak transition strengths in the nuclear medium in the case of the quasielastic reactions. The inelastic reactions leading to production of leptons along with pions is calculated in a $\Delta $- dominance model by taking into account the renormalization of $\Delta$ properties in the nuclear medium and the final state interaction effects of the outgoing pions with the residual nucleus. We have presented the results for the lepton events obtained in our model with and without nuclear medium effects, and compare them with the Monte Carlo predictions used in the simulation and the experimentally observed events reported by the Super-Kamiokande collaboration. B. MiniBooNE and K2K collaborations have recently reported the ratio for the $\nu_\mu$ induced charge current 1$\pi^+$ production cross section to the charged current induced quasielastic lepton production cross section i.e. $R(E)=\frac{\sigma^{CC1\pi^+}}{\sigma^{CCQE}}$. We have studied, theoretically, in a local density approximation the effect of nuclear medium in charged current quasielastic(CCQE) and charged current one pion production(CC1$\pi^+$) processes for the $\nu_\mu$ induced reaction in nuclei. The theoretical results have been compared with the results of experimental observations by the MiniBooNE and K2K collaborations. The ratio R(E) for $\nu_\mu$ induced reaction in water for the proposed T2K experiment is also presented. C. The weak kaon production off the nucleon induced by neutrinos is studied at the low and intermediate energies of interest for some ongoing and future neutrino oscillation experiments. This process is also potentially important for the analysis of proton decay experiments. We have developed a microscopical model based on the SU(3) chiral Lagrangians. The basic parameters of the model are fpi, the pion decay constant, Cabibbo's angle, the proton and neutron magnetic moments and the axial vector coupling constants for the baryons octet, D and F, that are obtained from the analysis of the semileptonic decays of neutron and hyperons. The studied mechanisms are the main source of kaon production for neutrino energies up to 1.2 to 1.5 GeV for the various channels and the cross sections are large enough to be amenable to be measured by experiments such as Minerva and T2K. D. We have studied the nuclear effects in the electromagnetic structure function F2(x,Q^2) in nuclei in the deep inelastic lepton nucleus scattering process by taking into account Fermi motion, binding, pion and rho meson cloud contributions. Calculations have been done in a local density approximation using relativistic nuclear spectral functions which include nucleon correlations for nuclear matter. The ratios over deuteron structure function are obtained and compared with the recent JLAB results for light nuclei that show a non trivial A dependence. The results also have been compared with some of the older experiments performed by EMC, NMC and BCDMS collaborations using intermediate mass nuclei.
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