Symmetry-guided large-scale shell-model theory

Abstract

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 the light p-shell systems, such as 6 Li, 8 B, 8 Be, 12 C, and 16 O, and sd-shell nuclei exemplified by 20 Ne, based on first-principle explorations; through the Hoyle state in 12 C and enhanced collectivity in intermediate-mass nuclei, 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 -plusshell model approaches, and cluster models, including the resonating-group method. 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, with a focus on emergent patterns in the framework of the ab initio SA-NCSM with no a priori assumptions.

Ab initio translationally invariant nonlocal one-body densities from no-core shell-model theory

“…Based on the set of variables from Eqs. (14) and (15), we use a Fourier transformation of the operator defined in Eq. (1) and the coordinates defined in Eq.…”

“…Defining b K and b q , we can infer that a dimensionless coordinate transformation must hold in the same fashion as the coordinate transformation defined in Eq. (14),…”

Physics of Nuclei: Key Role of an Emergent Symmetry

“…However, in ab initio calculations the complexity of the nuclear problem dramatically increases with the number of particles, and when expressed in terms of literally billions of shell-model basis states, the structure of a nuclear state is unrecognizable. But expressing it in a more informative basis, the symmetry-adapted collective basis [10,11], leads to a major breakthrough: in this article, we report on the very unexpected outcome from first-principle investigations of light to intermediate-mass nuclei (below the calcium region), namely, the incredible simplicity of nuclear low-lying states and the dominance we observe of an associated symmetry of nuclear dynamics, the symplectic Sp(3, R) symmetry, which together with its slight symmetry breaking is shown here to naturally describe atomic nuclei. This exposes for the first time the fundamental role of the symplectic Sp(3, R) symmetry and unveils it as a remarkably good symmetry of the strong nuclear force, represented here by interactions derived in the state-of-the-art chiral effective field theory.…”

Ab initio folding potentials for nucleon-nucleus scattering based on no-core shell-model one-body densities

“…These nuclei have a ground state that is dominated by spin zero and often the spin-zero component is found to be in excess of 80% of the total wave function (e.g., see Table 3 in Ref. [25] for calculations using NNLO opt and another realistic interaction). For example, for 6 He, calculations at N max = 12 show that the zero-spin contribution to the ground state is about 80-85%.…”

“…Among other successful many-body theories, the ab initio no-core shell-model (NCSM) approach, which has considerably advanced our understanding and capability of achieving first-principles descriptions of low-lying states in light nuclear systems (e.g., see [19][20][21][22][23]), has over the last decade taken center stage in the development of microscopic tools for studying the structure of atomic nuclei. The NCSM concept combined with a symmetry-adapted (SA) basis in the ab initio SA-NCSM [24] has further expanded the reach to the structure of intermediate-mass nuclei [25].…”