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Symmetry-guided large-scale shell-model theory

In this review, we present a symmetry-guided strategy that utilizes exact as well as partial symmetries for enabling a deeper understanding of and advancing ab initio studies for determining the microscopic structure of atomic nuclei. These symmetries expose physically relevant degrees of freedom that, for large-scale calculations with QCD-inspired interactions, allow the model space size to be reduced through a very structured selection of the basis states to physically relevant subspaces. This can guide explorations of simple patterns in nuclei and how they emerge from first principles, as well as extensions of the theory beyond current limitations toward heavier nuclei and larger model spaces. This is illustrated for the ab initio symmetry-adapted no-core shell model (SA-NCSM) and two significant underlying symmetries, the symplectic Sp(3,R) group and its deformation-related SU(3) subgroup. We review the broad scope of nuclei, where these symmetries have been found to play a key role: from light to intermediate-mass nuclei, based on first-principle explorations; through the Hoyle state in C-12, within a no-core shell-model perspective; up to strongly deformed species of the rare-earth and actinide regions, as investigated in earlier studies. A complementary picture, driven by symmetries dual to Sp(3,R), is also discussed. We briefly review symmetry-guided techniques that prove useful in various nuclear-theory models, such as Elliott model, ab initio SA-NCSM, symplectic model, pseudo-SU(3) and pseudo-symplectic models, ab initio hyperspherical harmonics method, ab initio lattice effective field theory, exact pairing-plus-shell model approaches, and cluster models. Important implications of these approaches that have deepened our understanding of emergent phenomena in nuclei, such as enhanced collectivity, giant resonances, pairing, halo, and clustering, are discussed.