The low-lying excited states of ${}^{10}$Be and ${}^{12}$Be are investigated within a no-core Monte Carlo shell-model (MCSM) framework employing a realistic potential obtained via the unitary correlation operator method. The excitation energies of the $2_1^{+}$ and $2_2^{+}$ states and the $B(E2;2_{1,2}^{+}\to 0_{g.s.}^{+})$ value for ${}^{10}$Be in the MCSM with a standard treatment of spurious center-of-mass motion show good agreement with experimental data. Some properties of low-lying states of ${}^{10}$Be are studied in terms of quadrupole moments, $E2$ transitions, and single-particle occupation numbers. The $E2$ transition probability of ${}^{10}$C, the mirror nucleus of ${}^{10}$Be, is also presented with a good agreement to experiment. The triaxial deformation of ${}^{10}$Be and ${}^{10}$C is discussed in terms of the $B\left(E2\right)$ values. The removal of the spurious center-of-mass motion affects various states differently: for instance, it has a negligible effect on the $2_1^{+}$ and $2_2^{+}$ levels of ${}^{10}$Be, while it leads to a significant and favorable shift for the $1_1^{-}$ level. It is suggested that the description of ${}^{12}$Be needs a larger model space as well as some other higher excited states of ${}^{10}$Be, as an indicator that these are dominated by intruder configurations.

• Received 24 April 2011

DOI:https://doi.org/10.1103/PhysRevC.86.014302