For Be and C isotopes with $N>8$, the shell-model study with $2\hslash \omega$ basis states shows the enhancement of neutron quadrupole matrix elements. The neutron-rich nuclei such as ${}^{14}\mathrm{Be}$ and ${}^{16}\mathrm{C}$ have a few neutrons in the $1s_{1/2}$ and $0d_{5/2}$ orbits, and the neutrons in these orbits give the large neutron quadrupole motion because these orbits have almost the same single-particle energies. A large ratio of proton and neutron quadrupole matrix elements in these nuclei indicates decoupled motions of proton and neutron, which are suggested in the measurements of the $B(E2)$ values.

• Received 2 November 2007

DOI:https://doi.org/10.1103/PhysRevC.77.044301