No-Core MCSM calculation for ${}^{10}$Be and ${}^{12}$Be low-lying spectra

Abstract

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${}_{g.s.}^{+}$) 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(E2) values. The removal of the spurious center-of-mass motion affects differently on various states: for instance, negligible effects on the 2${}_1^{+}$ and 2${}_2^{+}$ levels of ${}^{10}$Be, while 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.