Relativistic treatment of the charged-current reaction ${}^{12}{\rm C}(ν_μ,μ^{-})$ near threshold

Abstract

We compute the cross section for the charged-current reaction ${}^{12}{\rm C}(ν_μ,μ^{-})$ near threshold using a relativistic mean-field formalism. A reduced value of the nucleon mass in the medium --- coupled to the finite muon mass --- leads to a 30\% reduction in the cross section relative to a free Fermi-gas estimate. Isovector RPA correlations, which are strongly repulsive at these momentum transfers, reduce the cross section by an additional 15-30\%. Hence, relativistic nuclear-structure effects can account for the more than a factor-of-two reduction in the cross section recently reported by the LSND collaboration.