Neutrino and antineutrino cross sections in ${}^{12}$C

Abstract

We extend the formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, both for neutrino-nucleus reactions and muon capture. We have done a thorough study of exclusive (ground state) properties of ${}^{12}$B and ${}^{12}$N within the projected quasiparticle random phase approximation (PQRPA). Good agreement with experimental data is achieved in this way. The inclusive neutrino/antineutrino ($\nu /\tilde{\nu }$) reactions ${}^{12}$C($\nu ,e^{-}{)}^{12}$N and ${}^{12}$C($\tilde{\nu },e^{+}{)}^{12}$B are calculated within both the PQRPA, and the relativistic QRPA (RQRPA). It is found that the magnitudes of the resulting cross-sections: i) are close to the sum-rule limit at low energy, but significantly smaller than this limit at high energies both for $\nu$ and $\tilde{\nu }$, ii) they steadily increase when the size of the configuration space is augmented, and particulary for $\nu /\tilde{\nu }$ energies $>200$ MeV, and iii) converge for sufficiently large configuration space and final state spin.

Comments: Proceedings of the International Nuclear Physics Conference 2010, Vancouver, BC - Canada 4-9 Jul 2010