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

TL;DR

This paper develops new formalism for weak interaction processes to accurately calculate neutrino and antineutrino cross sections on carbon-12, validating results with experimental data and exploring energy dependence.

Contribution

It introduces improved expressions for transition rates and applies advanced nuclear models to compute cross sections, enhancing accuracy and computational efficiency.

Findings

Cross sections are close to sum-rule limits at low energies.

Cross sections increase with larger configuration spaces, especially above 200 MeV.

Results converge with sufficiently large configuration spaces.

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.