Nuclear Dynamics and Reactions in the Ab Initio Symmetry-Adapted Framework

Abstract

We review the ab initio symmetry-adapted (SA) framework for determining the structure of stable and unstable nuclei, along with related electroweak, decay, and reaction processes. This framework utilizes the dominant symmetry of nuclear dynamics, the shape-related symplectic SP(3,ℝ) symmetry, which has been shown to emerge from first principles and to expose dominant degrees of freedom that are collective in nature, even in the lightest species or seemingly spherical states. This feature is illustrated for a broad scope of nuclei ranging from helium to titanium isotopes, enabled by recent developments of the ab initio SA no-core shell model expanded to the continuum through the use of the SA basis and that of the resonating group method. The review focuses on energies, electromagnetic transitions, quadrupole and magnetic moments, radii, form factors, and response function moments for ground-state rotational bands and giant resonances. The method also determines the structure of reaction fragments that is used to calculate decay widths and α-capture reactions for simulated X-ray burst abundance patterns, as well as nucleon–nucleus interactions for cross sections and other reaction observables. Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 71 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Efficacy of the symmetry-adapted basis for ab initio nucleon-nucleus interactions for light- and intermediate-mass nuclei

“…[70]. This allows the mixing of all possible shapes within the complete subspaces, whereas the higher selected subspaces accommodate spatially expanded collective modes [9].…”

“…5), which is feasible for no-core shell-model calculations with the importance truncation using other interactions [76]. In our study, we use the NNLO sat [77], for which the three-nucleon (3N) forces are included in the SA-NCSM as averages [9]. Namely, in these calculations, the 3N forces are included as a mass-dependent monopole interaction [78], which has an effect on binding energies.…”

“…In particular, the symmetry-adapted no-core shell-model (SA-NCSM) [1, 2] uses a physically relevant symmetry-adapted (SA) basis that can achieve significantly reduced model spaces compared to the corresponding complete ultra-large model spaces, without compromising the accuracy of results for various observables [1,3,4]. This enables the SA-NCSM to accommodate contributions from more shells and to describe heavier nuclei, such as 20 Ne [2], 21 Mg [5], 22 Mg [6], 28 Mg [7], as well as 32 Ne and 48 Ti [8,9]. The access to higher-lying shells makes the SA basis suitable for describing nuclear reactions [9], the processes that are typically studied in experiments and govern stellar evolution.…”

Machine learning approach to pattern recognition in nuclear dynamics from the ab initio symmetry-adapted no-core shell model

“…Ab initio approaches use controlled approximations and interactions informed by the few-nucleon physics only, and therefore, they are suitable to determine reaction rates used in simulations of astrophysical processes, which involve shortlived nuclei that are impossible or difficult to be measured. With the symmetry-adapted no-core shell model (SA-NCSM) [1,2], ab initio calculations have been made possible up to the calcium region by utilizing symmetries that are inherent to atomic nuclei [3]. However, reaching even heavier nuclei remains a challenge.…”

“…N is the total number of HO excitation quanta. The deformation is represented by λ and µ quantum numbers, which inform how prolate and oblate a state is, that is, (λ 0) indicates a prolate deformation, (0 µ) indicates an oblate deformation, whereas (0 0) denotes a spherical shape [2,3]. The label κ distinguishes multiple occurrences of the same orbital momentum L in a given (λ µ).…”