Effects of energy levels on the double-differential cross sections for \(n + ^{13}\)C reaction below 20 MeV

The nuclear data of \(n + ^{13}\)C reaction are very important in describing the evolution of nuclear astrophysics, understanding the cluster structure of light nuclei, and producting the radiocarbon. Based on the unified Hauser-Feshbach and exciton model, a statistical theory of light nucleus reaction (STLN) is improved to describe the effects of energy levels on the double-differential cross sections of neutron and charged particles for \(n + ^{13}\)C reaction. The individual contributions of every energy level of the target and different residual nuclei have been analysed. The calculated results agree well with all of the existing experimental double-differential cross sections of outgoing neutron. And the theoretical analysis provides an evidence for the existence of the possible levels of \(^{13}\)C. The results also indicate that the contributions of the direct inelastic scattering derived from DWBA theory and the three-body breakup reaction should be considered. Especially, the contributions of (n, 2n) channel of the 6-th energy level of \(^{13}\)C have been considered. The doubt regarding the significant discrepancies observed near 3-MeV exit energy range for two closely spaced incident energies of 8.09 MeV and 8.24 MeV has been clarified. Furthermore, the total double-differential cross sections of outgoing proton, deuteron, triton, and \(\alpha \) can be self-consistently predicted at arbitrary outgoing angles and incident energies for \(n+^{13}\text {C}\) reaction.