Examination of collective and single-particle models for excited states of $^{13}$C below 10 MeV in nuclear reactions induced by 18 MeV deuteron beam

Abstract

This paper presents a study of both the elastic and inelastic scattering of a deuteron beam on $^{13}$C at laboratory energy of 18 MeV. The first 10 excited states of the carbon isotope were studied in terms of single-particle and collective models of excitation. Experimental cross sections were obtained by the well-known $\Delta$E–E method. Elastic scattering data were analyzed using an optical model including a nucleus–nucleus interaction potential, while inelastic scattering data were processed using the coupled-channels approach. For the single-particle model, the spectroscopic amplitudes were obtained through calculations of the large-scale shell model with the YSOXT effective NN-potential. A double folding potential was obtained for the d + $^{13}$C system. A comparison of model calculations with the experimental cross sections was demonstrated. The extracted deformation parameters and calculated spectroscopic information are shown in tables. The ability of the collective model to describe all excited states was demonstrated by good agreement when comparing the calculated cross sections in the collective model and experimental data. The single-particle model turned out to be significant only for the excited state of 3.09 MeV. The dominant role in the formation of the corresponding cross section is played by the $^{12}$C ground state core with the 2$S_{1/2}$ neutron.