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

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 $\widehat{Q}$-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.

Figure 1

${}^{19}\mathrm{C}$ experimental [14, 15, 16] and calculated levels by the GSM and the real-energy SM (indicated by SM) using the same CD-Bonn interaction. The resonance state is marked by shadowing with the resonance width (in MeV) given above the level.

Figure 2

Similar to Fig. 1 but for ${}^{20,22}\mathrm{C}$. The data are from [33, 47].

Figure 3

Similar to Fig. 1 but for ${}^{21}\mathrm{C}$. There is no excited state observed experimentally except the ($1/2^{+}$) ground state [49].

Figure 4

Calculated effective single-particle energies for the neutron $1s_{1/2}$, $0d_{5/2}$, $0d_{3/2}$ orbitals.

Figure 5

Experimental [33] and calculated ground-state energies with respect to the ${}^{14}\mathrm{C}$ core. The RSM calculations without and with the single-particle energy (s.p.e.) shift are from Ref. [20]. The VS-IMSRG results are from [21]. Data shown with open circles are evaluations taken from [33].