Realistic Gamow shell-model calculations for neutron-rich carbon isotopes

Abstract

The weakly bound nuclei near the drip-line have many interesting properties which have been the hot spot for current nuclear physics research. Carbon isotopes can reach a high neutron to proton ratio and could be a good example to investigate the weakly bound and unbound nuclei. The drip-line nucleus 22C is the heaviest Borromean nucleus that people have observed and corresponds to a sub-shell at neutron number N =16 which is also observed in nitrogen and oxygen isotopes. For nuclei close to drip-line, the coupling of bound-, resonant- and continuum states becomes particularly important. But the traditional shell models with harmonic-oscillator basis are difficult to describe the resonant- and continuum states because the harmonic-oscillator potential always has a localized wave function and bound-eigenstates. One of the ways to include the continuum effects is employing the Berggren basis which is generated by finite potential like Woods-Saxon potential. With Berggren basis, the Schrodinger equation is expanded to complex-momentum space and the bound-, resonant- and continuum states could be taken into account on an equal footing. In addition, the necessity of chiral three-body forces has been shown in many ab-initio calculations like the reproducing of oxygen drip-line and low-lying spectrum of beryllium and boron isotopes. So it is meaningful to have a theoretical research of the carbon isotopes with considering both continuum effects and three-body forces. In this paper, we calculate the neutron-rich carbon isotopes with realistic Gamow shell model which starts from chiral N3LO two-body and chiral N2LO three-body forces. The three-body forces are included by normal-ordering approach. We use Woods-Saxon potential with 14C as a core to generate the Berggren basis. The parameters of Woods-Saxon potential are chosen to reproduce the single-particle energies close to experimental data. In Berggren basis, the continuum states are lying on the integral contour within the fourth quarter of complex-momentum space and discretized by Gauss-Legendre quadrature method for the further calculations. The effective interactions are built by Q ^ -box folded-diagram method within the model space of {1s1/2-bound, 0d5/2-bound, 0d3/2-resonance, d3/2-continuum, s1/2-continuum}. In order to deal with the large dimensions caused by the introducing of continuum states, we take an approximation that only two or less particles are allowed to occupy the continuum states. The ground states energies and the first 2+ excitation energies are calculated for even-mass carbon isotopes from A =16 to A =24 and achieve a good agreement with the experimental data. With our calculations, the 22C is shown to be the last bound even- A carbon isotope. In addition, by investigating the evolution of the first 2+ states, our results agree with the experiment that the sub-shell at N =14 in oxygen isotopes is observed to disappear in carbon isotopes, meanwhile the sub-shell at N =16 is reproduced by our calculations. Furthermore, we compare the ground states energies calculated with and without three-body forces and find out that the three-body forces will make the results more weakly bound and more consistent with experimental values especially for 22C and 24C. Meanwhile, the resonance widths which are calculated self-consistently by realistic Gamow shell model become broader. So our calculations give a support that the three-body forces will introduce a repulsive effect in neutron rich carbon isotopes and play a key role when describing the nuclear drip-line.