Charged Lepton Production from Iron Induced by Atmospheric Neutrinos

The charged current lepton production induced by neutrinos in $^{56}Fe$ nuclei has been studied. The calculations have been done for the quasielastic as well as the inelastic reactions assuming $\Delta$ dominance and take into account the effect of Pauli blocking, Fermi motion and the renormalization of weak transition strengths in the nuclear medium. The quasielastic production cross section for lepton production are found to be strongly reduced due to nuclear effects while there is about 10% reduction in the inelastic cross sections in the absence of the final state interactions of the pions. The numerical results for the momentum and angular distributions of the leptons averaged over the various atmospheric neutrino spectra at the Soudan and Gransasso sites have been presented. The effect of nuclear model dependence and the atmospheric flux dependence on the relative yield of ${\mu}$ to e has been studied and discussed.