Quasi-Elastic Neutrino Reactions on Carbon and Lead Nuclei

We examine neutral-current quasi-elastic neutrino-nucleus reactions on $^{12}$C and $^{208}$Pb targets. We use the relativistic mean field theory approach to describe the nuclear dynamics. We compute the cross sections for the scattering of 150-MeV, 500-MeV and 1000-MeV neutrinos on a $^{12}$C target and study the effect of the strange-quark content of the nucleon which appears in these reactions via the isoscalar weak current. We compare our results with the data of the MiniBooNE experiment for mineral oil (CH$_2$). We also calculate the cross section for the quasi-elastic neutron knockout reaction of 20 to 60-MeV neutrinos on a $^{208}$Pb target which is relevant to plans to use lead as a target material in future supernova neutrino detectors.