Mean-field plus quadrupole–quadrupole and pairing model in the ds-shell

An algebraic framework for carrying out detailed shell model calculations in a SU(3) basis is introduced and applied to various sets of ds-shell valence nucleons bound in a shell model mean-field with residual quadrupole–quadrupole and pairing interactions. Binding energies, experimentally known low-lying positive parity energy levels as well as electric quadrupole moments, magnetic dipole moments, B(E2) and B(M1) values of $$^{17-22}$$ O and $$^{17}$$ F, $$^{18}$$ Ne, $$^{19}$$ Na, $$^{20}$$ Mg, $$^{21}$$ Al, $$^{22}$$ Si are fit and compared to the corresponding experimental results. It is shown that the binding energies of these nuclei are fit well by the model with the quality of the fit to the low-lying energy levels similar to that of the shell model using the USD interaction. It is also shown that the overall data pattern of the results fits to the known electric quadrupole moments, magnetic dipole moments, B(E2) and B(M1) values follow that of the experimental data with only a few exceptions. In addition, the ground-state dynamic shape of these nuclei is estimated with the correspondence between the Bohr $$(\beta ,\gamma )$$ variables and the SU(3) irreducible representation $$(\lambda \,\mu )$$ . The results show that the nuclei in the ds-shell approaching the neutron or proton drip line tend to be triaxially unstable with relatively stronger pairing interactions.