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.