Microscopic theories of neutrino-¹²C reactions

In view of the recent experiments on neutrino oscillations performed by the LSND and KARMEN Collaborations as well as future experiments, we present new theoretical results of the flux-averaged ¹²C(ν_e,e^-)¹²N and ¹²C(ν_μ,μ^-)¹²N cross sections. The approaches used are charge-exchange random-phase approximation (RPA), charge-exchange RPA among quasiparticles (QRPA), and the shell model. With a large-scale shell-model calculation the exclusive cross sections are in nice agreement with the experimental values for both reactions. The inclusive cross section for ν_μ coming from the decay-in-flight of π⁺ is 15.2× 10^-40 cm² (when Hartree-Fock wave functions are used), to be compared to the experimental value of 12.4±0.3±1.8 ×10^-40 cm², while the one due to ν_e coming from the decay-at-rest of μ⁺ is 16.4×10^-42 cm² which agrees within experimental error bars with the measured values. The shell-model prediction for the decay-in-flight neutrino cross section is reduced compared to the RPA one, namely 19.2×10^-40 cm². This is mainly due to the different kind of correlations taken into account in the calculation of the spin modes (in particular, because of the quenching in the 1⁺ channel) and partially due to the shell-model configuration basis which is not large enough, as we show using arguments based on sum rules. Results for exclusive and inclusive muon capture rates and β decay are given and are close to the experimental findings.