Program in C for studying characteristic properties of two-body interactions in the framework of spectral distribution theory

We present a program in C that employs spectral distribution theory for studies of characteristic properties of a many-particle quantum-mechanical system and the underlying few-body interaction. In particular, the program focuses on two-body nuclear interactions given in a JT-coupled harmonic oscillator basis and calculates correlation coefficients, a measure of similarity of any two interactions, as well as Hilbert-Schmidt norms specifying interaction strengths. An important feature of the program is its ability to identify the monopole part (centroid) of a 2-body interaction, as well as its 'density-dependent' one-body and two-body part, thereby providing key information on the evolution of shell gaps and binding energies for larger nuclear systems. As additional features, we provide statistical measures for 'density-dependent' interactions, as well as a mechanism to express an interaction in terms of two other interactions. This, in turn, allows one to identify, e.g., established features of the nuclear interaction (such as pairing correlations) within a general Hamiltonian. The program handles the radial degeneracy for 'density-dependent' one-body interactions and together with an efficient linked list data structure, facilitates studies of nuclear interactions in large model spaces that go beyond valence-shell applications.Comment: 22 pages, 3 figure

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

We present an ab initio symmetry-adapted no-core shell-model description for $^{6}$Li. We study the structure of the ground state of $^{6}$Li and the impact of the symmetry-guided space selection on the charge density components for this state in momentum space, including the effect of higher shells. We accomplish this by investigating the electron scattering charge form factor for momentum transfers up to $q \sim 4$ fm$^{-1}$. We demonstrate that this symmetry-adapted framework can achieve significantly reduced dimensions for equivalent large shell-model spaces while retaining the accuracy of the form factor for any momentum transfer. These new results confirm the previous outcomes for selected spectroscopy observables in light nuclei, such as binding energies, excitation energies, electromagnetic moments, E2 and M1 reduced transition probabilities, as well as point-nucleon matter rms radii.Comment: 10 pages, 7 figures; accepted to Physical Review

Ab initio symmetry-adapted no-core shell model

A multi-shell extension of the Elliott SU(3) model, the SU(3) symmetry-adapted version of the no-core shell model (SA-NCSM), is described. The significance of this SA-NCSM emerges from the physical relevance of its SU(3)-coupled basis, which - while it naturally manages center-of-mass spuriosity - provides a microscopic description of nuclei in terms of mixed shape configurations. Since typically configurations of maximum spatial deformation dominate, only a small part of the model space suffices to reproduce the low-energy nuclear dynamics and hence, offers an effective symmetry-guided framework for winnowing of model space. This is based on our recent findings of low-spin and high-deformation dominance in realistic NCSM results and, in turn, holds promise to significantly enhance the reach of ab initio shell models

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.Comment: 9 pages, 8 figure

Symmetry-adapted ab initio shell model for nuclear structure calculations

An innovative concept, the symmetry-adapted ab initio shell model, that capitalizes on partial as well as exact symmetries that underpin the structure of nuclei, is discussed. This framework is expected to inform the leading features of nuclear structure and reaction data for light and medium mass nuclei, which are currently inaccessible by theory and experiment and for which predictions of modern phenomenological models often diverge. 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. This, in turn, points to the importance of using a symmetry-adapted framework, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation

Symmetry-adapted Ab initio theory for many-body correlations in nuclei

We demonstrate that no-core shell-model results for low-lying states of light and medium mass nuclei, whether they are dilute or dense systems, reveal a strong dominance of low-spin and high-deformation configurations. This result is independent of whether the system Hamiltonian is phenomenological in nature or derived from a realistic interaction. It implies that only a small fraction of the complete model space is required for a description of such states, and this in turn points to the importance of using a symmetry-adapted, no-core shell-model framework for describing such nuclei, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation. These results confirm that the pioneering work of early developers of the field, J. P. Elliott with his SU(3) model and M. Moshinsky with his U(3) many-body oscillator work, extends to more open, multi-shell environments. Specifically, algebraic methods are both relevant in such an environment and they can be used to quell the combinatorial growth in dimensionality that comes with the addition of oscillator shells to a model space. Indeed, our findings demonstrate the utility of a symmetry-adapted, no-core shell-model approach, one that takes advantage of group theoretical as well as advanced computational methods. And importantly, what at first glance appear to be a daunting task - casting complex algebraic expressions of a symmetry-adapted scheme into a user-friendly and efficient shell-mode code, turns out to be not only doable, but a logical framework that embraces constructs that can be made to execute efficiently on massively parallel, multi-processor (and core) systems. Early results for some light p-shell nuclei are presented. In addition, we will show that the method can be extended to heavier nuclei of the sd-shell and beyond, including some cases of special astrophysical interest in the upper fp- and lower gds-shells, like isotopes of Ge, Se, and even Kr. © Published under licence by IOP Publishing Ltd

Ab initio No-core Shell Model Calculations in a SU(3)-based Coupling Scheme

We use powerful algorithms of computational group theory to perform ab initio configuration-interaction calculations in a SU(3)-based symmetry-adapted many-particle basis. We demonstrate that eigenfunctions for the low-lying states of 6Li, 8Be, 12C, and 16O exhibit a strong dominance of low proton, neutron, and total intrinsic spins that carry the same spatial deformation as the leading symplectic Sp(3,) irreducible representations. Our findings imply that only a small fraction of the complete model space is needed to model nuclear collective dynamics, deformation, 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 framework, one based on a LS coupling scheme with the associated spatial configurations organized according to deformation. © Published under licence by IOP Publishing Ltd

Ab initio symmetry-adapted emulator for studying emergent collectivity and clustering in nuclei

We discuss emulators from the ab initio symmetry-adapted no-core shell-model framework for studying the formation of alpha clustering and collective properties without effective charges. We present a new type of an emulator, one that utilizes the eigenvector continuation technique but is based on the use of symplectic symmetry considerations. This is achieved by using physically relevant degrees of freedom, namely, the symmetry-adapted basis, which exploits the almost perfect symplectic symmetry in nuclei. Specifically, we study excitation energies, point-proton root-mean-square radii, along with electric quadrupole moments and transitions for 6Li and 12C. We show that the set of parameterizations of the chiral potential used to train the emulators has no significant effect on predictions of dominant nuclear features, such as shape and the associated symplectic symmetry, along with cluster formation, but slightly varies details that affect collective quadrupole moments, asymptotic normalization coefficients, and alpha partial widths up to a factor of two. This makes these types of emulators important for further constraining the nuclear force for high-precision nuclear structure and reaction observables

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 SU(3)-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.Comment: 11 pages, 8 figure