<italic>Ab initio</italic> calculations of nuclear systems

Abstract

<p indent=0mm>Thanks to the advanced radioactive beam facilities, weakly-bound and unbound nuclei have been explored in an unprecedented way. Most of these exotic nuclei belong to the category of open quantum systems, hence coupling to the particle continuum profoundly affects their behaviors. Many novel phenomena have been observed or predicted in the exotic nuclei, such as genuine intrinsic resonances, halos and shell evolutions. They provide ideal laboratories to test advanced many-body methods. In particular, due to the low particle-emission threshold, the continuum coupling should be properly treated in the description of weakly-bound and unbound nuclei. In the meanwhile, with the development of chiral effective field theory and quantum many-body theory, nuclear<italic> ab initio</italic> calculations have made great progress in the past decade. Conventionally, <italic>ab initio</italic> calculations are usually performed in the harmonic-oscillator (HO) or HO-based Hartree-Fock (HF) basis. However, the HO basis is bound and localized, which is isolated from the environment of scattering states and cannot describe the exotic properties of drip-line nuclei properly. Hence, it is still a challenge to describe open quantum systems efficiently, especially for <italic>ab initio</italic> methods. The main difficulty focuses on how to include the coupling to the scattering continuum. Among several approaches, Berggren basis is a very elegant choice, since it generalizes the one-body Schrodinger equation to a complex-momentum plane and then treats bound, resonant and continuum states on an equal footing. Besides, a lot of theoretical work has shown the three-nucleon force could play an important role, especially in nuclei around the drip lines. Thus, this kind of <italic>ab initio</italic> method for weakly-bound or unbound nuclei should properly treat continuum effects, three-nucleon force and many-nucleon correlations. The present paper reviews our recent work on the realistic Gamow shell model with a core (CGSM) to study the location of the nuclear drip lines, the role of three-nucleon force and the halo structure. Starting from the chiral two- and three-nucleon forces, the CGSM takes advantage of the <italic>ab initio</italic> many-body perturbation theory (called nondegenerate <italic>Q</italic>-box folded-diagram renormalization) within the Berggren basis to derive an effective Hamiltonian in a valence model space. Then the effective Hamiltonian is diagonalized by the complex Gamow shell model. Resonance and continuum properties of loosely-bound or unbound nuclear systems can be well studied by this kind of calculation. We have presented the results of oxygen isotopes carried out by CGSM, in which the weakly-bound and resonant properties are obtained. The calculations indicate that continuum coupling and three-nucleon force are both important for the oxygen isotopes around drip-line region. For the frontier calcium chain, CGSM gives the drip line of calcium locates at ⁷⁰Ca. Furthermore, the exotic properties of the shell evolutions in the long calcium chain have been investigated. Our calculations show good agreements with experimental data within <italic>N</italic>=32 and <italic>N</italic>=34 closure shells, and predict the weakness of <italic>N</italic>=40 shell in calcium chain. At last, the two-proton halo structure of ¹⁷Ne is suggested in CGSM calculations, and both the continuum effect and the three-nucleon force are shown to be essential for the halo property of ¹⁷Ne.