Comparative experimental study of the mirror ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$${+}^{12}$C and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${+}^{12}$C elastic scatterings

The ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ elastic cross sections are measured at the center-of-mass energies of 7.8, 9.6, and 14.2 MeV, using radioactive ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ and stable ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ beams and position-sensitive solid-state detectors. These data are analyzed with the optical model assuming the same real central part of the nuclear potential for both systems as suggested by charge symmetry. The ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ angular distributions display a significant backward rise which arises from a parity dependence of the nucleus-nucleus interaction, as for the mirror ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ system. The corresponding parity terms in both potentials are similar when the different charges of the exchanged nucleons and their different binding energies are properly taken into account. A smaller imaginary part is obtained for ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ than for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, which might be due to a smaller number of open two-body inelastic and direct reaction channels.