We study boron, carbon, nitrogen, and oxygen isotopes with a newly constructed shell-model Hamiltonian developed from a monopole-based universal interaction ($V_{MU}$). The present Hamiltonian can reproduce well the ground-state energies, energy levels, electric quadrupole properties, and spin properties of these nuclei in full $psd$ model space including $(0-3)\hslash \omega$ excitations. Especially, it correctly describes the drip lines of carbon and oxygen isotopes and the spins of the ground states of ${}^{10}$B and ${}^{18}$N while some former interactions such as WBP and WBT fail. We point out that the inclusion of $2\hslash \omega$ excitations is important in reproducing some of these properties. In the present $(0+2)\hslash \omega$ calculations small but constant $E2$ effective charges appear to work quite well. As the inclusion of the $2\hslash \omega$ model space makes a rather minor change, this seems to be related to the smallness of the ${}^4$He core. Similarly, the spin $g$ factors are very close to free values. The applicability of tensor and spin-orbit forces in free space, which are taken in the present Hamiltonian, is examined in shell-model calculations.

• Received 17 April 2012

DOI:https://doi.org/10.1103/PhysRevC.85.064324