Emergent symmetries in atomic nuclei from first principles

An innovative symmetry-guided approach and its applications to light and intermediate-mass nuclei is discussed. This approach, with Sp(3, R) the underpinning group, is based on our recent remarkable finding, namely, we have identified the symplectic Sp(3,R) as an approximate symmetry for low-energy nuclear dynamics. This study presents the results of two complementary studies, one that utilizes realistic nucleon-nucleon interactions and unveils symmetries inherent to nuclear dynamics from first principles (or ab initio), and another study, which selects important components of the nuclear interaction to explain the primary physics responsible for emergent phenomena, such as enhanced collectivity and alpha clusters. In particular, within this symmetry-guided framework, ab initio applications of the theory to light nuclei reveal the emergence of a simple orderly pattern from first principles. This provides a strategy for determining the nature of bound states of nuclei in terms of a relatively small fraction of the complete shell-model space, which, in turn, can be used to explore ultra-large model spaces for a description of alpha-cluster and highly deformed structures together with associated rotations. We find that by using only a fraction of the model space extended far beyond current no-core shell-model limits and a long-range interaction that respects the symmetries in play, the outcome reproduces characteristic features of the low-lying 0+ states in 12C (including the elusive Hoyle state of importance to astrophysics) and agrees with ab initio results in smaller spaces. For these states, we offer a novel perspective emerging out of no-core shell-model considerations, including a discussion of associated nuclear deformation, matter radii, and density distribution. The framework we find is also extensible beyond 12C, namely, to the low-lying 0+ states of 8Be as well as the ground-state rotational band of Ne, Mg, and Si isotopes

SU(3)-guided Realistic Nucleon-nucleon Interactions for Large-scale Calculations

We examine nucleon-nucleon realistic interactions, based on their SU(3) decomposition to SU(3)-symmetric components. We find that many of these interaction components are negligible, which, in turn, allows us to identify a subset of physically relevant components that are sufficient to describe the structure of low-lying states in $^{12}$C and related observables, such as excitation energies, electric quadrupole transitions and rms radii. We find that paring the interaction down to half of the SU(3)-symmetric components or more yields results that practically coincide with the corresponding ab initio calculations with the full interaction. In addition, we show that while various realistic interactions differ in their SU(3) decomposition, their renormalized effective counterparts exhibit a striking similarity and composition that can be linked to dominant nuclear features such as deformation, pairing, clustering, and spin-orbit effect.Comment: 9 pages, 7 figure

Electromagnetic Excitations and Responses in Nuclei from First Principles

We discuss the role of clustering on monopole, dipole, and quadrupole excitations in nuclei in the framework of the ab initio symmetry-adapted no-core shell model (SA-NCSM). The SA-NCSM starts from nucleon-nucleon potentials and, by exploring symmetries known to dominate the nuclear dynamics, can reach nuclei up through the calcium region by accommodating ultra-large model spaces critical to descriptions of clustering and collectivity. The results are based on calculations of electromagnetic sum rules and discretized responses using the Lanczos algorithm, that can be used to determine response functions, and for 4He are benchmarked against exact solutions of the hyperspherical harmonics method. In particular, we focus on He, Be, and O isotopes, including giant resonances and monopole sum rules.Comment: 6 pages, 4 figures, Proceedings of the Fourth International Workshop on State of the Art in Nuclear Cluster Physics, Galveston, TX, USA, May 13-18, 201

Electromagnetic Excitations and Responses in Nuclei from First Principles

We discuss the role of clustering on monopole, dipole, and quadrupole excitations in nuclei in the framework of the ab initio symmetry-adapted no-core shell model (SA-NCSM). The SA-NCSM starts from nucleon-nucleon potentials and, by exploring symmetries known to dominate the nuclear dynamics, can reach nuclei up through the calcium region by accommodating ultra-large model spaces critical to descriptions of clustering and collectivity. The results are based on calculations of electromagnetic sum rules and discretized responses using the Lanczos algorithm, that can be used to determine response functions, and for 4He are benchmarked against exact solutions of the hyperspherical harmonics method. In particular, we focus on He, Be, and O isotopes, including giant resonances and monopole sum rules.Comment: 6 pages, 4 figures, Proceedings of the Fourth International Workshop on State of the Art in Nuclear Cluster Physics, Galveston, TX, USA, May 13-18, 201

No-core Symplectic Model: Exploiting Hidden Symmetry in Atomic Nuclei

We report on recent developments within the framework of the no-core symplectic shell model (NCSpM) that complements the no-core shell model (Navrátil, Vary, and Barrett) by exploiting the algebraic features of the symplectic shell model (Rowe and Rosensteel) while also allowing for high-performance computing applications, but in highly truncated, physically relevant subspaces of the complete space. The leading symplectic symmetry typically accounts for 70% to 90% of the structure of the low-lying states, a result that is only moderately dependent on the details of the selected inter-nucleon interaction. Examples for6Li,12C,16O, and20Ne are shown to illustrate the efficacy the NCSpM, and as well the strong overlap with cluster-like and pairing configurations that dominate the dynamics of low-lying states in these nuclei

Nuclear spin features relevant to ab initio nucleon-nucleus elastic scattering

Background: Effective interactions for elastic nucleon-nucleus scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations, as well as a consistent treatment of the relevant operators at each order. Purpose: Previous work using these interactions has shown good agreement with available data. Here, we study the physical relevance of one of these operators, which involves the spin of the struck nucleon, and examine the interpretation of this quantity in a nuclear structure context. Methods: Using the framework of the spectator expansion and the underlying framework of the no-core shell model, we calculate and examine spin-projected, one-body momentum distributions required for effective nucleon-nucleus interactions in $J=0$ nuclear states. Results: The calculated spin-projected, one-body momentum distributions for $^4$He, $^6$He, and $^8$He display characteristic behavior based on the occupation of protons and neutrons in single particle levels, with more nucleons of one type yielding momentum distributions with larger values. Additionally, we find this quantity is strongly correlated to the magnetic moment of the $2^+$ excited state in the ground state rotational band for each nucleus considered. Conclusions: We find that spin-projected, one-body momentum distributions can probe the spin content of a $J=0$ wave function. This feature may allow future \textit{ab initio} nucleon-nucleus scattering studies to inform spin properties of the underlying nucleon-nucleon interactions. The observed correlation to the magnetic moment of excited states illustrates a previously unknown connection between reaction observables such as the analyzing power and structure observables like the magnetic moment.Comment: 13 pages, 7 figures, 1 tabl

Ab initio Leading Order Effective Potentials for Elastic Nucleon-Nucleus Scattering

Background: Calculating microscopic effective interactions (optical potentials) for elastic nucleon-nucleus scattering has already in the past led to a large body of work. For first-order calculations a nucleon-nucleon (\textit{NN}) interaction and a one-body density of the nucleus were taken as input to rigorous calculations of microscopic full-folding calculations. Purpose: Based on the spectator expansion of the multiple scattering series we employ a chiral next-to-next-to-leading order (NNLO) nucleon-nucleon interaction on the same footing in the structure as well as in the reaction calculation to obtain an in leading-order consistent effective potential for nucleon-nucleus elastic scattering, which includes the spin of the struck target nucleon. Methods: The first order effective folding potential is computed by first deriving a nonlocal scalar density as well as a spin-projected momentum distribution. Those are then integrated with the off-shell Wolfenstein amplitudes $A$, $C$, and $M$. The resulting nonlocal potential serves as input to a momentum-space Lippmann-Schwinger equation, whose solutions are summed to obtain the nucleon-nucleus scattering observables. Results: We calculate elastic scattering observables for $^4$He, $^6$He, $^8$He, $^{12}$C, and $^{16}$O in the energy regime between 100 and 200 MeV projectile kinetic energy, and compare to available data. We also explore the extension down to about 70 MeV, and study the effect of ignoring the spin of the struck nucleon in the nucleus. Conclusions: In our calculations we contrast elastic scattering off closed-shell and open-shell nuclei. We find that for closed-shell nuclei the approximation of ignoring the spin of the struck target nucleon is excellent. We only see effects of the spin of the struck target nucleon when considering $^6$He and $^8$He, which are nuclei with a $N/Z$ ratio larger than 1.Comment: 13 pages, 13 figure