Next-generation Symmetry-adapted Shell Model for Light and Medium Mass Nuclei*

Construction of a comprehensive next-generation fully microscopic shell model to explore collective features of atomic nuclei at low energy is presented. The theoretical foundation thereof takes maximum advantage of Wigner’s Supermultiplet Symmetry (WSS), which was proposed from the early days of nuclear structure studies, nonetheless, still attracting interests across a wide range of subatomic physics – especially in the high-energy community owing to the emergence of WSS at leading orders of chiral nucleon-nucleon forces. Within this framework, the model space is factored into two sectors: i) the spatial part dominated by Elliott’s U(3) symmetry capturing excitations, and ii) the spin-isospin part unified under U(4) WSS embracing intrinsic characters of nucleons. The construction of such a comprehensive model requires the coupling of basis states within each sector of the model space. With the efforts of an extended LSU team, a modern methodology for the U(3) part has recently been proposed in [Dang et al, EPJP 139, 704 (2024)]; meanwhile, on the U(4) side, a streamline and accurate computer package has also been proffered in [Dang et al, EPJP, accepted], which was heretofore unavailable due to the complex underlying algebraic structure. With these two state-of-the-art packages in hand, a new symmetry-adapted shell model, once constructed, should enable a deeper understanding of the much-debated behavior of nuclear forces and how they are connected to the strong interaction.