We extend the ab initio coupled-cluster effective interaction (CCEI) method to open-shell nuclei with protons and neutrons in the valence space and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei ${}^{20}\mathrm{Ne}$ and ${}^{24}\mathrm{Mg}$, we reproduce rotational bands and electric quadrupole transitions within uncertainties estimated from an effective field theory for deformed nuclei, thereby demonstrating that collective phenomena in $sd$-shell nuclei emerge from complex ab initio calculations.

• Received 4 November 2015
• Revised 16 May 2016

DOI:https://doi.org/10.1103/PhysRevC.94.011301