T. Dytrych

Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei

Clear evidence for symplectic symmetry in low-lying states of 12C and 16O is reported. Eigenstates of 12C and 16O, determined within the framework of the no-core shell model using the J-matrix inverse scattering potential with A<or=16 (JISP16) nucleon-nucleon (NN) realistic interaction, typically project at the 85%-90% level onto a few of the most deformed symplectic basis states that span only a small fraction of the full model space. The results are nearly independent of whether the bare or renormalized effective interactions are used in the analysis. The outcome confirms Elliotts SU(3) model which underpins the symplectic scheme, and above all, points to the relevance of a symplectic no-core shell model that can reproduce experimental B(E2) values without effective charges as well as deformed spatial modes associated with clustering phenomena in nuclei.

Ab initio symplectic no-core shell model

The no-core shell model (NCSM) is a prominent ab initio method that yields a good description of the low-lying states in few-nucleon systems as well as in more complex p-shell nuclei. Nevertheless, its applicability is limited by the rapid growth of the many-body basis with larger model spaces and increasing number of nucleons. The symplectic no-core shell model (Sp-NCSM) aspires to extend the scope of the NCSM beyond the p-shell region by augmenting the conventional spherical harmonic oscillator basis with the physically relevant symplectic symmetry-adapted configurations of the symplectic shell model that describe naturally the monopole?quadrupole vibrational and rotational modes, and also partially incorporate ?-cluster correlations. In this review, the models underpinning the Sp-NCSM approach, namely, the NCSM, the Elliott SU(3) model and the symplectic shell model, are discussed. Following this, a prescription for constructing translationally invariant symplectic configurations in the spherical harmonic oscillator basis is given. This prescription is utilized to unveil the extent to which symplectic configurations enter into low-lying states in 12C and 16O nuclei calculated within the framework of the NCSM with the JISP16 realistic nucleon?nucleon interaction. The outcomes of this proof-of-principle study are presented in detail.

Hoyle state and rotational features in Carbon-12 within a no-core shell model framework

Abstract By using only a fraction of the model space extended beyond current no-core shell-model limits and a many-nucleon interaction with a single parameter, we gain additional insight within a symmetry-guided shell-model framework, into the many-body dynamics that gives rise to the ground state rotational band together with phenomena tied to alpha-clustering substructures in the low-lying states in 12C, and in particular, the challenging Hoyle state and its first 2 + and 4 + excitations. For these states, we offer a novel perspective emerging out of no-core shell-model considerations, including a discussion of associated nuclear deformation and matter radii. This, in turn, provides guidance for ab initio shell models by informing key features of nuclear structure and the interaction.

Collective modes in light nuclei from first principles.

Results for ab initio no-core shell model calculations in a symmetry-adapted SU(3)-based coupling scheme demonstrate that collective modes in light nuclei emerge from first principles. The low-lying states of 6Li, 8Be, and 6He are shown to exhibit orderly patterns that favor spatial configurations with strong quadrupole deformation and complementary low intrinsic spin values, a picture that is consistent with the nuclear symplectic model. The results also suggest a pragmatic path forward to accommodate deformation-driven collective features in ab initio analyses when they dominate the nuclear landscape.

Symplectic No-core Shell-model Approach to Intermediate-mass Nuclei

We present a microscopic description of nuclei in an intermediate-mass region, including the proximity to the proton drip line, based on a no-core shell model with a schematic many-nucleon long-range interaction with no parameter adjustments. The outcome confirms the essential role played by the symplectic symmetry to inform the interaction and the winnowing of shell-model spaces. We show that it is imperative that model spaces be expanded well beyond the current limits up through fifteen major shells to accommodate particle excitations that appear critical to highly-deformed spatial structures and the convergence of associated observables.

Highly deformed modes in the ab initio symplectic no-core shell model

We show that highly deformed modes essential for nuclear dynamics modeling can readily be included in the symplectic no-core shell model (Sp-NCSM) space. In particular, a prescription for constructing general deformed k-particle–k-hole (kp–kh) translationally invariant symplectic starting state configurations and symplectic excitations thereof in a fermion-based spherical harmonic oscillator basis is presented. This prescription is used to build the symplectic excitations over all possible as well as the most deformed configurations in 12C and 16O. The extent to which these configurations enter into low-lying states for these nuclei calculated within the framework of the no-core shell model with a realistic microscopic interaction is then determined. Typically, the addition of these and representations to the leading results grow the overall overlap with the no-core-shell-model eigenstates by 5–10% for a total of 85–90%. And most importantly, even with the addition of these higher-order particle–hole configurations, the dimensionality of the symplectic subspace constitutes a very small fraction of the conventional full no-core shell model space, which reaffirms the relevance of the Sp-NCSM scheme.

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 s d -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–plus–shell 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.

Electron-scattering form factors for Li 6 in the ab initio symmetry-guided framework

We present an ab initio symmetry-adapted no-core shell-model description for

Efficacy of the SU(3) scheme for ab initio large-scale calculations beyond the lightest nuclei

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Block iterators for sparse matrices

Li. We study the structure of the ground state of