RPA Puzzle in 12 C Weak Decay Processes

We explain the origin of the difficulties that appear in a straightforward application of the QRPA in 12 C, and we demonstrate that it is imperative to use the projected QRPA (PQRPA). Satisfactory results, not only for the weak processes among the ground states of the triad { 12 B, 12 C, 12 N }, but also for the inclusive ones are obtained. We sketch as well a new formalism for the neutrino-nucleus interaction that furnishes very simple final formulae for the muon capture rate and neutrino induced cross sections. New types of nuclear weak processes have been measured in recent years. They are based on neutrino and antineutrino interactions with complex nuclei and, rather than being used to study the corresponding cross sections, they are mainly aimed to inquire on possible exotic properties of neutrino themselves, such as neutrino oscillations and the associate neutrino massiveness, which are not contained in the Standard Model (SM) of elementary particles. So, in neutrino oscillation experiments with liquid scintillators, the charge-exchange reactions 12 C(ν e , e −) 12 N and 12 C(ν µ , µ −) 12 N, both exclusive (to the 1 + ground state) and inclusive (to all final states), are just tools. As such, and to be useful, the corresponding cross sections σ exc e,µ and σ inc e,µ must be accurately accounted for by nuclear structure models. ¿From the recent works [1, 2, 3, 4] we have learned, however, that neither RPA nor QRPA are able to explain the weak processes (β-decays, µ-capture, and neutrino induced reactions) among the ground states of the triad { 12 B, 12 C, 12 N }. In fact, in the RPA a rescaling factor of the order of 4 is needed to bring the calculations and data in agreement [1], and a subsequent 1