On the algebraic formulation of collective models III. The symplectic shell model of collective motion

Rosensteel, G.; Rowe, D.J.

doi:10.1016/0003-4916(80)90180-3

Cited by 262 publications

(135 citation statements)

References 21 publications

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“…Indeed, experimental evidence supports the fact that in this mass range, the dynamics favors a dominance of low spin and high deformation, which has been demonstrated by symmetry-guided theoretical studies [4][5][6] as well as through an ab initio study [8,15]. The latter exploits symplectic symmetry and its deformationrelated SU(3) subgroup in an analysis of ab initio largescale nuclear physics applications for 12 C and 16 O.…”

Section: Introductionmentioning

confidence: 87%

“…In particular, we employ the no-core symplectic (NCSpM) shell model for symmetrypreserving interactions [2] with Sp(3, R) the underpinning symmetry [3]. This symmetry is inherent to the dynamics of deformed nuclear systems [4][5][6][7][8]. The present study uses a schematic, but fully microscopic and physically motivated effective many-nucleon interaction, a choice that enables the use of group-theoretical methods with analytical expressions for Hamiltonian matrix elements, and which in turn makes large space solutions for sd-shell nuclei feasible.…”

Section: Introductionmentioning

confidence: 99%

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Symplectic no-core shell-model approach to intermediate-mass nuclei

et al. 2014

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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.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Symplectic no-core shell-model approach to intermediate-mass nuclei

et al. 2014

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“…These considerations motivate us to develop and investigate a novel model, the ab initio symmetry-adapted no-core shell model (SA-NCSM) [18], which, by taking advantage of symmetries inherent to the nuclear dy- * Corresponding author:dytrych@ujf.cas.cz namics [19][20][21][22], can provide access to heavier nuclei and larger model spaces essential to accommodate collective, deformed, and cluster substructures [22][23][24][25][26][27][28][29][30][31][32]. This is achieved by recognizing that the choice of a basis is crucial and that the SA-NCSM affords a solution that is a linear combination of a limited number of basis states of definite nuclear deformation.…”

Section: Introductionmentioning

confidence: 99%

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

Dytrych

Maris

Launey

et al. 2016

Computer Physics Communications

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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 6 Li and 12 C 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.

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“…The symplectic model [16,17] is an algebraic model whose dynamical group Sp(3, R) comprises all n-independent linear canonical transformations of the single-particle phase-space observableŝ…”

Section: The Symplectic Modelmentioning

confidence: 99%

The fundamental role of symmetry in nuclear models

Rowe

2013

AIP Conference Proceedings

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Abstract. The purpose of these lectures is to illustrate how symmetry and pattern recognition play essential roles in the progression from experimental observation to an understanding of nuclear phenomena in terms of interacting neutrons and protons. We do not discuss weak interactions nor relativistic and sub-nucleon degrees of freedom. The explicit use of symmetry and the power of algebraic methods, in combination with analytical and geometrical methods are illustrated by their use in deriving a shell-model description of nuclear rotational dynamics and the structure of deformed nuclei.

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On the algebraic formulation of collective models III. The symplectic shell model of collective motion

Cited by 262 publications

References 21 publications

Symplectic no-core shell-model approach to intermediate-mass nuclei

Symplectic no-core shell-model approach to intermediate-mass nuclei

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

The fundamental role of symmetry in nuclear models

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