Neutrino- ¹² C reactions and the LSND and KARMEN experiments on neutrino oscillations

We present new theoretical results of the flux-averaged ¹² C(ν _e , e ^- ) ¹² N and ¹² C(ν _μ , μ ^- ) ¹² N cross sections with ν _μ (ν _e ) coming from the decay-in-flight (decay-at-rest) of π ⁺ (μ ⁺ ). These cross sections are relevant for the interpretation of the recent experiments on neutrino oscillation performed by the LSND and KARMEN collaborations. The microscopic approaches used are charge-exchange random phase approximation (RPA), charge-exchange RPA among quasiparticles (QRPA), and the Shell Model. We show that the exclusive cross sections are in nice agreement with the experimental values for both reactions when a large-scale shell-model calculation is performed. Concerning the inclusive cross section for ν _μ coming from the decay-in-flight of π ⁺ , the calculated value keeps overestimating the experimental one by 20-30%, while the inclusive cross section due to ν _e coming from the decay-at-rest of μ ⁺ is in agreement 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 because of the different kind of correlations in the calculation of the spin modes (in particular, the quenching of the 1 ⁺ ) and partially due to the shell-model configuration basis, which is not large enough, as we show using arguments based on sum rules.