An investigation of ab initio shell-model interactions derived by no-core shell model

The microscopic shell-model effective interactions are mainly based on the many-body perturbation theory （MBPT）, the first work of which can be traced to Brown and Kuo＇s first attempt in 1966, derived from the Hamada-Johnstou nucleon-nucleon potential. However, the convergence of the MBPT is still unclear. On the other hand, ab initio theories, such as Green＇s function Monte Carlo （GFMC）, no-core shell model （NCSM）, and coupled-cluster theory with single and double excitations （CCSD）, have made many progress in recent years. However, due to the increasing demanding of computing resources, these ab initio applications are usually limited to nuclei with mass up to A = 16. Recently, people have realized the ab initio construction of valence-space effective interactions, which is obtained through a second-time renormalization, or to be more exactly, projecting the full-many- body Hamiltonian into core, one-body, and two-body cluster parts. In this paper, we present the investigation of such ab initio shell-model interactions, by the recent derived sd-shell effective interactions based on effective J-matrix Inverse Scattering Potential （JISP） and chiral effective-field theory （EFT） through NCSM. In this work, we have seen the similarity between the ab initio shell- model interactions and the interactions obtained by MBPT or by empirical fitting. Without the inclusion of three-body （3-bd） force, the ab initio shell-model interactions still share similar defects with the microscopic interactions by MBPT, i.e., T = 1 channel is more attractive while T = 0 channel is more repulsive than empirical interactions. The progress to include more many-body correlations and 3-bd force is still badly needed, to see whether such efforts of ab initio shell-model interactions can reach similar precision as the interactions fitted to experimental data.

The microscopic shell-model effective interactions are mainly based on the many-body perturbation theory(MBPT), the first work of which can be traced to Brown and Kuo's first attempt in 1966, derived from the Hamada-Johnston nucleon-nucleon potential.However, the convergence of the MBPT is still unclear. On the other hand, ab initio theories, such as Green's function Monte Carlo(GFMC), no-core shell model(NCSM), and coupled-cluster theory with single and double excitations(CCSD), have made many progress in recent years. However, due to the increasing demanding of computing resources, these ab initio applications are usually limited to nuclei with mass up to A = 16. Recently, people have realized the ab initio construction of valence-space effective interactions, which is obtained through a second-time renormalization, or to be more exactly, projecting the full-manybody Hamiltonian into core, one-body, and two-body cluster parts. In this paper, we present the investigation of such ab initio shell-model interactions, by the recent derived sd-shell effective interactions based on effective J-matrix Inverse Scattering Potential(JISP) and chiral effective-field theory(EFT) through NCSM. In this work, we have seen the similarity between the ab initio shellmodel interactions and the interactions obtained by MBPT or by empirical fitting. Without the inclusion of three-body(3-bd) force,the ab initio shell-model interactions still share similar defects with the microscopic interactions by MBPT, i.e., T = 1 channel is more attractive while T = 0 channel is more repulsive than empirical interactions. The progress to include more many-body correlations and 3-bd force is still badly needed, to see whether such efforts of ab initio shell-model interactions can reach similar precision as the interactions fitted to experimental data.