Multichannel dynamical symmetry and heavy ion resonances

Cseh, J.

doi:10.1103/physrevc.50.2240

Cited by 45 publications

(89 citation statements)

References 21 publications

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“…It is more probable that they are located in the local minima corresponding to the superdeformed [SD(p): the very low-energy part] and mainly to the triaxial (Tri) shape. In [32] the detailed spectra of the 24 Mg + 4 He and 16 O + 12 C cluster configurations were described in a unified way in terms of the multichannel dynamical symmetry of the semimicroscopic algebraic cluster model. A renewed study of that kind would be interesting in light of the recent developments on the shape isomers.…”

Section: B Structural Selectionmentioning

confidence: 99%

Shape isomers and clusterization in the28Si nucleus

2012

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Section: B Structural Selectionmentioning

confidence: 99%

Shape isomers and clusterization in the28Si nucleus

2012

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“…This rigorous derivation results in the same energy functional, which was obtained in a phenomenological way in Ref. [5].…”

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confidence: 54%

“…This rigorous derivation results in the same energy functional, which was obtained in a phenomenological way in Ref. [5].In what follows, first we recall the basic features of the SACM and the empirical introduction of the MUSY, then we go step-by-step in its rigorous derivation. The example we consider involves the 16 …”

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confidence: 72%

“…In Ref. [5] the multichannel dynamical symmetry (MUSY) was introduced to describe this phenomenon. Here the channel refers to the reaction channel, which defines a binary cluster configuration.…”

mentioning

confidence: 99%

“…Here the channel refers to the reaction channel, which defines a binary cluster configuration. The idea was invented at the phenomenological level, based on general physical arguments, which resulted in relations for the energy eigenvalues [5]. However, the mathematical background, and the exact physical nature of this new symmetry, has not been revealed so far.…”

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Multichannel dynamical symmetry and cluster-coexistence

Cseh¹,

Katō²

2013

Phys. Rev. C

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A composite symmetry of the nuclear structure, called multichannel dynamical symmetry, is established. It can describe different cluster configurations (defined by different reaction channels) in a unified framework; thus, it has a considerable predictive power. The two-channel case is presented in detail, and its conceptual similarity to the dynamical supersymmetry is discussed. [5] the multichannel dynamical symmetry (MUSY) was introduced to describe this phenomenon. Here the channel refers to the reaction channel, which defines a binary cluster configuration. The idea was invented at the phenomenological level, based on general physical arguments, which resulted in relations for the energy eigenvalues [5]. However, the mathematical background, and the exact physical nature of this new symmetry, has not been revealed so far. Here we present the scenario of how one can establish the algebraic structure of the MUSY in general, and we give a detailed derivation for the two-channel dynamical symmetry.To illustrate the main features of this new symmetry it seems to be proper to recall some basic vocabulary on symmetries. A continuous symmetry is an exact one if the Hamiltonian commutes with the generators of its Lie group. A dynamical symmetry is said to hold if the Hamiltonian can be expressed in terms of the invariant operators of a chain of nested subgroups (see, e.g., Refs. [6][7][8](Sometimes this symmetry is called a dynamically broken symmetry, because only G f is an exact symmetry.) In such a case the eigenvalue problem of the energy has an analytical solution, and the labels of irreducible representations are good quantum numbers.Let us consider a system of two components (1 and 2), each of them described by an algebraic model and having (at least one) dynamical symmetry: G i ⊃ G i ⊃ G i ⊃ · · ·; i = 1, 2. If the particle numbers of the two components are conserved separately, then the algebraic model with group structure G 1 ⊗ G 2 usually proves to be a successful approach. The subgroups of G 1 ⊗ G 2 define the relevant dynamical symmetries of the system.Deeper symmetries, with different nature, arise from the embedding of the direct product group into a larger group: G 0 ⊃ G 1 ⊗ G 2 . Some generators of G 0 transform particles of type 1 into particles of type 2, or vice versa. In this article we refer to a composite symmetry in this sense. In the supermultiplet scheme of Wigner, e.g., the protons and neutrons are not conserved separately [1,3]. In the SUSY models collective phonons and nucleons are transformed into each other because of the embedding into graded Lie algebras [U(6/m) ⊃ U(6) ⊗ U(m) in the quadrupole [2,3], and U(4/m) ⊃ U(4) ⊗ U(m) in the dipole, i.e., cluster models [4]].The multichannel dynamical symmetry is formulated in the framework of the semimicroscopic algebraic cluster model (SACM) [9], in which the clusterization of atomic nuclei is described in a fully algebraic way. The model space is constructed microscopically; thus, one can take into account that the antisymmetrization may wa...

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Multichannel Dynamic Symmetry

Cseh

1997

Symmetries in Science IX

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Multichannel dynamical symmetry and heavy ion resonances

Cited by 45 publications

References 21 publications

Shape isomers and clusterization in the28Si nucleus

Shape isomers and clusterization in the28Si nucleus

Multichannel dynamical symmetry and cluster-coexistence

Multichannel Dynamic Symmetry

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