Low-energy spectra of mirror mass-19 nuclei with a collective coupled-channel scattering model

Abstract

The spectra of mass-19 nuclei are unusual and pose a challenge for theoretical models of their structure. Herein the Multi-Channel Algebraic Scattering (MCAS) method has been used with a collective (vibrational model) description of the low-excitation states of $$^{18}$$ O and $$^{18}$$ Ne to describe the spectra of four mass-19 nuclei, specifically the mirror pairs ( $$^{19}$$ O, $$^{19}$$ Na) and ( $$^{19}$$ F, $$^{19}$$ Ne). This coupled-channel approach allows for the effects of the Pauli principle to be included using non-local orthogonalizing pseudo-potentials. By the coupling of neutrons to the core nuclei, we obtain states in $$^{19}$$ O (a neutron coupled to $$^{18}$$ O) and $$^{19}$$ Ne (a neutron coupled to $$^{18}$$ Ne). Mirror symmetry and addition of the Coulomb interaction gives states in $$^{19}$$ F (a proton coupled to $$^{18}$$ O) and $$^{19}$$ Na (a proton coupled to $$^{18}$$ Ne). However, the same compound nuclei may be described as the coupling of more complicated nuclear clusters. We obtain the states in $$^{19}$$ F as the coupling of an $$\alpha $$ to $$^{15}$$ N, as well as the coupling of $$^3$$ H to $$^{16}$$ O. Similarly, states in $$^{19}$$ Ne have been obtained from the coupling of an $$\alpha $$ to $$^{15}$$ O and of the coupling of $${}^3$$ He to $$^{16}$$ O. Finally, as the method allows extraction of scattering matrices, it has been used to evaluate cross sections for the elastic scattering of low-energy neutrons from $$^{18}$$ O and of low-energy $$\alpha $$ particles from $$^{15}$$ O.