Microscopic theories of neutrino-12Creactions

Abstract

In view of the recent experiments on neutrino oscillations performed by the LSND and KARMEN collaborations as well as of future experiments, we present new theoretical results of the flux averaged 12 C(νe, e − ) 12 N and 12 C(νµ, µ − ) 12 N cross sections. The approaches used are charge-exchange RPA, charge-exchange RPA among quasi-particles (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 νµ coming from the decay-in-flight of π + is 15.2 × 10 −40 cm 2 (when Hartree-Fock wavefunctions are used), to be compared to the experimental value of 12.4 ± 0.3 ± 1.8 × 10 −40 cm 2 , while the one due to νe coming from the decay-at-rest of µ + is 16.4 × 10 −42 cm 2 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 cm 2 . 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 beta decay are given and are close to the experimental findings.

Inclusive and pion production neutrino-nucleus cross sections

“…At large angles the contribution of the collective states is suppressed by form factor effects [22]. Several studies have been made on the excitation of low energy collective states in neutrino interactions [22][23][24][25][26][27][28] but specific work is needed to assess their role in the present type of data where forward bins offer favorable conditions to display their contribution.…”

Nuclear structure and neutrino-nucleus interaction

“…In fact, the SM calculation performed by Hayes and Towner [11] reproduces fairly well several data. But, in a later SM study, Volpe et al [12] noted that this concordance could be an artifact because the employed model space was not large enough to exhaust the charge-exchange sum rules. More, the same authors have shown that when a more extended space is employed the SM cross sections are increased exceeding the experimental LSND result.…”

“…The GT sum rule limit SR GT [7] and several previous RPA-like calculations, namely: RPA [12], CRPA [17], and RQRPA within S 20 for two-quasiparticle cutoff E 2qp =100 MeV [9], PQRPA within S 2 , S 3 , and S 6 [7], as well as the shell model result [12], are also exhibited.…”

“…Therefore in this case the energies were derived in the way done in Ref. [9], while the pairing strengths were adjusted to reproduce the experimental gaps in 12 C, considering all the quasiparticle energies up to 100 MeV.…”

“…Nuclei are often used as neutrino detectors, and in particular 12 C which is a component of many scintillator detectors. [2,3].…”