Large basis ab initio shell model investigation of 9Be and 11Be

We present the first ab initio structure investigation of the loosely bound $^{11}\mathrm{Be}$ nucleus, together with a study of the lighter isotope $^{9}\mathrm{Be}$. The nuclear structure of these isotopes is particularly interesting because of the appearance of a parity-inverted ground state in $^{11}\mathrm{Be}$. Our study is performed in the framework of the ab initio no-core shell model. Results obtained using four different, high-precision two-nucleon interactions, in model spaces up to $9\ensuremath{\hbar}\ensuremath{\Omega}$, are shown. For both nuclei, and all potentials, we reach convergence in the level ordering of positive- and negative-parity spectra separately. Concerning their relative position, the positive-parity states are always too high in excitation energy, but a fast drop with respect to the negative-parity spectrum is observed when the model space is increased. This behavior is most dramatic for $^{11}\mathrm{Be}$. In the largest model space we were able to reach, the $1/{2}^{+}$ level has dropped down to become either the first or the second excited state, depending on which interaction we use. We also observe a contrasting behavior in the convergence patterns for different two-nucleon potentials and argue that a three-nucleon interaction is needed to explain the parity inversion. Furthermore, large-basis calculations of $^{13}\mathrm{C}$ and $^{11}\mathrm{B}$ are performed. This allows us to study the systematics of the position of the first unnatural-parity state in the $N=7$ isotone and the $A=11$ isobar. The $^{11}\mathrm{B}$ run in the $9\ensuremath{\hbar}\ensuremath{\Omega}$ model space involves a matrix with dimension exceeding $1.1\ifmmode\times\else\texttimes\fi{}{10}^{9}$, and is our largest calculation so far. We present results on binding energies, excitation spectra, level configurations, radii, electromagnetic observables, and $^{10}\mathrm{Be}+n$ overlap functions.