Symmetry-adapted No-core Shell Model Research Articles

Uncertainty quantification of collective nuclear observables from the chiral potential parametrization

We perform an uncertainty estimate of quadrupole moments and B(E2) transition rates that inform nuclear collectivity. In particular, we study the low-lying states of 6Li and 12C using the ab initio symmetry-adapted no-core–shell model. For a narrow standard deviation of approximately 1% on the low-energy constants which parametrize high-precision chiral potentials, we find output standard deviations in the collective observables ranging from approximately 3%–6%. The results mark the first step towards a rigorous uncertainty quantification of collectivity in nuclei that aims to account for all sources of uncertainty in ab initio descriptions of challenging collective and clustering observables.

Ab initio leading order effective potential for elastic proton scattering based on the symmetry-adapted no-core shell model

<i>Ab initio</i> leading order effective potential for elastic proton scattering based on the symmetry-adapted no-core shell model

New studies and predictions for nuclear clustering and dynamics in the ab initio symmetry-adapted framework

We discuss recent studies and predictions for nuclear clustering and dynamics within the framework of the ab initio symmetry-adapted no-core shell model, which has opened new domains of the nuclear chart. In this framework, we show the emergence from first principles of collectivity and clustering in light to mediummass nuclei, with implications for constructing ab initio optical potentials, for studying clustering in stable and unstable nuclei, for reproducing enhanced deformations without effective charges, and for the formation of clusters and its sensitivity to the underlying inter-nucleon force.

Parallel multithreaded deduplication of data sequences in nuclear structure calculations

High performance computing (HPC) applications that work with redundant sequences of data can benefit from their deduplication. We study this problem on the symmetry-adapted no-core shell model (SA-NCSM), where redundant sequences of different kinds naturally emerge in the data of the basis of the Hilbert space physically relevant to a modeled nucleus. For a fast solution of this problem on multicore architectures, we propose and present three multithreaded algorithms, which employ either concurrent hash tables or parallel sorting methods. Furthermore, we present evaluation and comparison of these algorithms based on experiments performed with real-world SA-NCSM calculations. The results indicate that the fastest option is to use a concurrent hash table, provided that it supports sequences of data as a type of table keys. If such a hash table is not available, the algorithm based on parallel sorting is a viable alternative.

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

A novel machine learning approach is used to provide further insight into atomic nuclei and to detect orderly patterns amidst a vast data of large-scale calculations. The method utilizes a neural network that is trained on ab initio results from the symmetry-adapted no-core shell model (SA-NCSM) for light nuclei. We show that the SA-NCSM, which expands ab initio applications up to medium-mass nuclei by using dominant symmetries of nuclear dynamics, can reach heavier nuclei when coupled with the machine learning approach. In particular, we find that a neural network trained on probability amplitudes for $s$-and $p$-shell nuclear wave functions not only predicts dominant configurations for heavier nuclei but in addition, when tested for the $^{20}$Ne ground state, it accurately reproduces the probability distribution. The nonnegligible configurations predicted by the network provide an important input to the SA-NCSM for reducing ultra-large model spaces to manageable sizes that can be, in turn, utilized in SA-NCSM calculations to obtain accurate observables. The neural network is capable of describing nuclear deformation and is used to track the shape evolution along the $^{20-42}$Mg isotopic chain, suggesting a shape-coexistence that is more pronounced toward the very neutron-rich isotopes. We provide first descriptions of the structure and deformation of $^{24}$Si and $^{40}$Mg of interest to x-ray burst nucleosynthesis, and even of the extremely heavy nuclei such as $^{166,168}$Er and $^{236}$U, that build upon first principles considerations.

Clustering and α -capture reaction rate from ab initio symmetry-adapted descriptions of Ne20

We introduce a new framework for studying clustering and for calculating alpha partial widths using ab initio wave functions. We demonstrate the formalism for $^{20}$Ne, by calculating the overlap between the $^{16}$O$+\alpha$ cluster configuration and states in $^{20}$Ne computed in the ab initio symmetry-adapted no-core shell model. We present spectroscopic amplitudes and spectroscopic factors, and compare those to no-core symplectic shell-model results in larger model spaces, to gain insight into the underlying physics that drives alpha-clustering. Specifically, we report on the alpha partial width of the lowest $1^-$ resonance in $^{20}$Ne, which is found to be in good agreement with experiment. We also present first no-core shell-model estimates for asymptotic normalization coefficients for the ground state, as well as for the first excited $4^{+}$ state in $^{20}$Ne that lies in a close proximity to the $^{16}$O$+\alpha$ threshold. This outcome highlights the importance of correlations for developing cluster structures and for describing alpha widths. The widths can then be used to calculate alpha-capture reaction rates for narrow resonances of interest to astrophysics. We explore the reaction rate for the alpha-capture reaction $^{16}$O$(\alpha,\gamma)^{20}$Ne at astrophysically relevant temperatures and determine its impact on simulated X-ray burst abundances.

Benchmark calculations of electromagnetic sum rules with a symmetry-adapted basis and hyperspherical harmonics

We demonstrate the ability to calculate electromagnetic sum rules with the \textit{ab initio} symmetry-adapted no-core shell model. By implementing the Lanczos algorithm, we compute non-energy weighted, energy weighted, and inverse energy weighted sum rules for electric monopole, dipole, and quadrupole transitions in $^4$He using realistic interactions. We benchmark the results with the hyperspherical harmonics method and show agreement within $2\sigma$, where the uncertainties are estimated from the use of the many-body technique. We investigate the dependence of the results on three different interactions, including chiral potentials, and we report on the $^4$He electric dipole polarizability calculated in the SA-NCSM that reproduces the experimental data and earlier theoretical outcomes. We also detail a novel use of the Lawson procedure to remove the spurious center-of-mass contribution to the sum rules that arises from using laboratory-frame coordinates. We further show that this same technique can be applied in the Lorentz integral transform method, with a view toward studies of electromagnetic reactions for light through medium-mass nuclei.

Overlaps of deformed and non-deformed harmonic oscillator basis states

A systematic approach for expanding non-deformed harmonic oscillator basis states in terms of deformed ones, and vice versa, is presented. The objective is to provide analytical results for calculating these overlaps (transformation brackets) between deformed and non-deformed basis states in spherical, cylindrical, and Cartesian coordinates. These overlaps can be used for reducing the complexity of different research problems that employ three-dimensional harmonic oscillator basis states, for example as used in coherent state theory and the nuclear shell-model, especially within the context of ab initio symmetry-adapted no-core shell model.

Structure of Mg28 and influence of the neutron pf shell

Gamma-ray spectroscopy and lifetime measurements using the Doppler shift attenuation method (DSAM) were performed on the nucleus $^{28}\mathrm{Mg}$ near the $N=20$ ``island of inversion,'' which was populated using a $^{12}\mathrm{C}(^{18}\mathrm{O},2\mathrm{p})^{28}\mathrm{Mg}$ fusion-evaporation reaction to investigate the impact of shell evolution on its high-lying structure. Three new levels were identified at 7203(3), 7747(2), and 7929.3(12) keV along with several new gamma rays. A newly extracted $B(E2;{4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ of 42(7) ${e}^{2}{\mathrm{fm}}^{4}$ indicates reduced collectivity in the yrast band at high spin, consistent with ab initio symmetry adapted no-core shell model (SA-NCSM) calculations. At high excitation energy, evidence for the population of intruder orbitals was obtained through identification of negative parity levels $[{I}^{\ensuremath{\pi}}={(0,4)}^{\ensuremath{-}}$, ${(4,5)}^{\ensuremath{-}}]$. Calculations using the SDPF-MU interaction indicate that these levels arise from single neutron excitation to the $pf$ shell and provides evidence for the lowering of these intruder orbitals approaching the island of inversion.

Accelerating many-nucleon basis generation for high performance computing enabled ab initio nuclear structure studies

We present the problem of generating a many-nucleon basis in [Formula: see text]-scheme for ab initio nuclear structure calculations in a symmetry-adapted no-core shell model framework. We first discuss and analyze the basis construction algorithm whose baseline implementation quickly becomes a significant bottleneck for large model spaces and heavier nuclei. The outcomes of this analysis are utilized to propose a new scalable version of the algorithm. Its performance is consequently studied empirically using the Blue Waters supercomputer. The measurements show significant acceleration achieved with over two orders of magnitude speedups realized for larger model spaces.

Importance Basis Truncation in the Symmetry-adapted No-core Shell Model

Importance Basis Truncation in the Symmetry-adapted No-core Shell Model

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

[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities. [Results:] A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of $^4$He, $^6$Li, $^{12}$C, and $^{16}$O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space [Conclusions:] We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms.

Importance Truncation in the SU(3) Symmetry-adapted No-core Shell Model

Importance Truncation in the SU(3) Symmetry-adapted No-core Shell Model

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

We report on the computational characteristics of ab initio nuclear structure calculations in a symmetry-adapted no-core shell model (SA-NCSM) framework. We examine the computational complexity of the current implementation of the SA-NCSM approach, dubbed LSU3shell, by analyzing ab initio results for 6Li and 12C in large harmonic oscillator model spaces and SU3-selected subspaces. We demonstrate LSU3shell’s strong-scaling properties achieved with highly-parallel methods for computing the many-body matrix elements. Results compare favorably with complete model space calculations and significant memory savings are achieved in physically important applications. In particular, a well-chosen symmetry-adapted basis affords memory savings in calculations of states with a fixed total angular momentum in large model spaces while exactly preserving translational invariance.

Emergence of Simple Patterns in Complex Atomic Nuclei from First Principles

We study the structure of low-lying states in 6Li, 6He, 8Be, 8B, 12C, and 16O, using ab initio symmetry-adapted no-core shell model. The results of our study demonstrate that collective modes in light nuclei emerge from first principles. We investigate the impact of the symmetry-adapted model space on spectroscopic properties and, in the case of the ground state of 6Li, on elastic electron scattering charge form factor. The results confirm that only a small symmetry-adapted subspace of the complete model space is needed to accurately reproduce complete-space observables and the form factor momentum dependence.

HPC-enabled Nuclear Structure Studies – Description and Applications of the Symmetry-adapted No-Core Shell Model

By exploiting symmetries that enable the accounting of vital collective correlations in nuclei, we achieve significantly reduced dimensions for equivalent ultra-large model spaces, and hence resolve the scale explosion problem in nuclear structure calculations, i.e, the explosive growth in computational resource demands with increasing number of particles and size of the spaces in which they reside. As a result, we provide – with the help of High Performance Computing (HPC) resources – first solutions for selected benchmark calculations with remarkable findings of large-deformation and low-spin dominance in low-lying nuclear states. In the framework of a complementary symmetry-adapted study, one is able, facilitated by symmetry-preserving pieces of the inter-nucleon interaction, to accommodate unprecedented shell-model spaces critical to capture the physics governing the Hoyle state in 12C, thereby addressing a 60-year-old puzzle on the emergence of cluster substructures within a no-core shell model framework. All of these findings underline the key role of symmetries in nuclear structure studies.

Dominant Modes in Light Nuclei - Ab Initio View of Emergent Symmetries

An innovative symmetry-guided concept is discussed with a focus on emergent symmetry patterns in complex nuclei. In particular, the ab initio symmetry-adapted no-core shell model (SA-NCSM), which capitalizes on exact as well as partial symmetries that underpin the structure of nuclei, provides remarkable insight into how simple symmetry patterns emerge in the many-body nuclear dynamics from first principles. This ab initio view is complemented by a fully microscopic no-core symplectic shell-model framework (NCSpM), which, in turn, informs key features of the primary physics responsible for the emergent phenomena of large deformation and alpha-cluster substructures in studies of the challenging Hoyle state in Carbon-12 and enhanced collectivity in intermediate-mass nuclei. Furthermore, by recognizing that deformed configurations often dominate the low-energy regime, the SA-NCSM provides a strategy for determining the nature of bound states of nuclei in terms of a relatively small subspace of the symmetry-reorganized complete model space, which opens new domains of nuclei for ab initio investigations, namely, the intermediate-mass region, including isotopes of Ne, Mg, and Si.

Symmetry-adapted ab initio no-core shell model calculations for 12C

Symmetry-adapted no-core shell-model calculations reveal dominant symmetry patterns in the structure of light nuclei, independent of whether the system Hamiltonian is phenomenological in nature or derived from realistic interactions. We show results of large-scale nuclear structure computations based on the ab initio symmetry-adapted no-core shell model that use only a fraction of the model space. In addition, the symmetry patterns unveiled in these results are employed to explore ultra-large model spaces for 12C. The outcome suggests a possible path forward for realizing collective theories that target correlated highly-deformed and alpha-cluster structures in terms of microscopic degrees of freedom that build forward from the nucleon-nucleon interaction itself.

Symmetry-Adapted Ab Initio Open Core Shell Model Theory

By using only a fraction of the model space, we gain further insight – within a symmetry-guided no-core shell model framework – into the many-body nuclear dynamics that gives rise to important single-particle configurations together with correlated highly-deformed and alpha-cluster structures. We show results of the novel ab initio symmetry-adapted no-core shell model for large-scale nuclear structure computations. In addition, we use the symmetry patterns unveiled in these results to explore ultra-large model spaces.

Symmetry-adapted no-core shell model applications for light nuclei with QCD-inspired interactions

We use powerful computational and group-theoretical algorithms to perform ab initio CI (configuration-interaction) calculations in a model space spanned by SU(3) symmetry-adapted many-body configurations with the JISP16 nucleon–nucleon interaction. We demonstrate that the results for the ground states of light nuclei up through A=16 exhibit a strong dominance of low-spin and high-deformation configurations together with an evident symplectic structure. We also find states among the lowest-lying 0+ eigenstates of 12C and 16O that are clearly dominated by α-clustering correlations. Our findings imply that only a small fraction of the full model space is needed to model nuclear collective dynamics, including deformations and α-particle clustering, even if one uses modern realistic interactions that do not preserve SU(3) symmetry. This, in turn, points to the importance of using a symmetry-adapted CI framework, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation.