Alpha and 8Be cluster amplitudes and core excitations in s-d shell nuclei

Hecht, K. T.

doi:10.1016/0375-9474(77)90429-8

Cited by 30 publications

(4 citation statements)

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“…This requires calculations of Hamiltonian ( Ô = A ĤA) and norm ( Ô = AA) kernels, which involve computations of overlaps of the type Ψ | Ô |Ψ (A properly takes into account antisymmetrization). In the SU(3)-based RGM framework of Hecht [207], the "localized" part of the kernels is reduced to calculating norm and Hamiltonian overlaps between the SU(3)-scheme RGM basis, which, e.g., for two fragments of mass number f and A − f can be written as,…”

Section: Resonating-group Methods (Rgm) In the Su(3) And Symplectic S...mentioning

confidence: 99%

“…As emphasized and shown in Refs. [207,208], the main advantage arises from the fact that the norm overlaps (both direct and exchange terms) are diagonal in this basis and that one can avoid the complications of embedding the angular momentum. Another important feature is that once the overlaps are calculated in labframe coordinates, the translationally-invariant overlaps can be straightforwardly calculated using an U(A)× U(3) approach, which is especially suitable for the SU(3)-coupled wave functions [207].…”

Section: Resonating-group Methods (Rgm) In the Su(3) And Symplectic S...mentioning

confidence: 99%

“…[207,208], the main advantage arises from the fact that the norm overlaps (both direct and exchange terms) are diagonal in this basis and that one can avoid the complications of embedding the angular momentum. Another important feature is that once the overlaps are calculated in labframe coordinates, the translationally-invariant overlaps can be straightforwardly calculated using an U(A)× U(3) approach, which is especially suitable for the SU(3)-coupled wave functions [207]. Applications of the model to the intermediate-mass region typically employ leading SU(3) configurations in the cluster wave functions and Gaussian-like interactions, and have successfully calculated α and 8 Be cluster amplitudes, spectroscopic amplitudes for heavy-fragment clusters, and sub-Coulomb 12 C+ 12 C resonances [209][210][211].…”

Section: Resonating-group Methods (Rgm) In the Su(3) And Symplectic S...mentioning

confidence: 99%

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Symmetry-guided large-scale shell-model theory

Launey

Dytrych

Draayer

2016

Progress in Particle and Nuclear Physics

131

173

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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 sd-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 -plusshell 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.

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Section: Resonating-group Methods (Rgm) In the Su(3) And Symplectic S...mentioning

confidence: 99%

Section: Resonating-group Methods (Rgm) In the Su(3) And Symplectic S...mentioning

confidence: 99%

Section: Resonating-group Methods (Rgm) In the Su(3) And Symplectic S...mentioning

confidence: 99%

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Symmetry-guided large-scale shell-model theory

Launey

Dytrych

Draayer

2016

Progress in Particle and Nuclear Physics

131

173

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“…All of these features make this method particularly suitable for unified descriptions of nuclear structure and reaction observables. Following the success of the Elliott model [32,33], showing that a leading (most deformed) SU(3) shell-model configuration describes reasonably well the ground-state rotational band in intermediate-mass nuclei, the RGM has been extensively used with an SU(3) basis and its nocore shell-model extension, the symplectic Sp(3, R) basis [34][35][36]. Applications of the model with Gaussian interactions have successfully calculated α and 8 Be cluster amplitudes, spectroscopic amplitudes for heavy-fragment clusters, and sub-Coulomb 12 C+ 12 C resonances [37][38][39].…”

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confidence: 99%

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

Mercenne,

Launey,

Dytrych

et al. 2021

Preprint

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We study the efficacy of a new ab initio framework that combines the symmetry-adapted (SA) no-core shell-model approach with the resonating group method (RGM) for unified descriptions of nuclear structure and reactions. We obtain ab initio neutron-nucleus interactions for 4 He, 16 O, and 20 Ne targets, starting with realistic nucleon-nucleon potentials. We discuss the effect of increasing model space sizes and symmetry-based selections on the SA-RGM norm and direct potential kernels, as well as on phase shifts, which are the input to calculations of cross sections. We demonstrate the efficacy of the SA basis and its scalability with particle numbers and model space dimensions, with a view toward ab initio descriptions of nucleon scattering and capture reactions up through the medium-mass region. I. INTRODUCTIONAb initio descriptions of spherical and deformed nuclei up through the calcium region are now possible within a no-core shell-model framework, by utilizing emerging symplectic symmetry in nuclei. 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. Remarkable progress has been made in firstprinciple descriptions to scattering and nuclear reactions for light nuclei (for an overview, see [10,11]), including studies of elastic scattering [12][13][14][15][16][17][18], photoabsorption [19], transfer [20] and capture reactions [21], α widths [22,23] and resonant states [24], as well as thermonuclear fusion [25]. In this paper, we show that expanding the reach of ab initio reactions to deformed and heavier targets is now feasible with the SA basis.

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SU3 symmetry and integral kernels for nuclear cluster problems

Hecht

Zahn

Group Theoretical Methods in Physics

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Alpha and 8Be cluster amplitudes and core excitations in s-d shell nuclei

Cited by 30 publications

References 55 publications

Symmetry-guided large-scale shell-model theory

Symmetry-guided large-scale shell-model theory

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

SU3 symmetry and integral kernels for nuclear cluster problems

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