Excitation spectra of the heaviest carbon isotopes investigated within the CD-Bonn Gamow shell model

Abstract

Neutron-rich carbon isotopes have been investigated within the Gamow shell model (GSM) based on a realistic nuclear force. $^{14}\mathrm{C}$ was chosen as the core in the shell-model calculations of the neutron-rich carbon isotopes. The effect from the coupling to the continuum is well considered by using the complex-momentum Berggren representation which treats bound, resonant, and continuum states on an equal footing. Using the many-body perturbation theory named the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{Q}$-box folded-diagram method, the complex GSM effective interaction was derived from the CD-Bonn interaction. We find that the inclusion of the continuum coupling in the calculation is important in the description of neutron-rich carbon isotopes, especially in reproducing the experimental $1/{2}^{+}$ ground states of $^{19}\mathrm{C}$ and $^{21}\mathrm{C}$. Our calculation indicates a shell closure at $N=16$ in the carbon chain, while the $N=14$ shell, which exists in the next even-$Z$ chain of oxygen isotopes, disappears. The calculation suggests that $^{22}\mathrm{C}$ is the heaviest bound carbon isotope, i.e., the neutron drip line.