The “cluster model” of the atomic nuclei

Wildermuth, K.; Kanellopoulos, Th. V.

doi:10.1016/0029-5582(58)90245-1

Cited by 265 publications

(197 citation statements)

References 20 publications

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“…Elliot has shown [1], how the quadrupole deformation and collective rotation can be derived from the spherical shell model: the states belonging to a collective band are determined by their specific S U(3) symmetry. Wildermuth and Kanellopoulos [2] established the relation between the shell and cluster models. They have shown that the Hamiltonians of the two models can be rewritten into each other exactly in the harmonic oscillator approximation.…”

Section: Preliminariesmentioning

confidence: 99%

Extreme quadrupole deformation and clusterization

Darai

Cseh

Adamian

et al. 2012

EPJ Web of Conferences

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Abstract. We discuss a simple symmetry-adapted method for the determination of the shape isomers, and for the study of their possible fragmentation. In other words the connection between the quadrupole (collective) and dipole (cluster) degrees of freedom is considered in terms of an easily applicable, yet microscopic method. The energetics is taken into account by the double-folding method. Special attention is focused on those cases in which the theoretical predictions have a direct comparison with experimental observation.

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Section: Preliminariesmentioning

confidence: 99%

Extreme quadrupole deformation and clusterization

Darai

Cseh

Adamian

et al. 2012

EPJ Web of Conferences

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“…The excited states of atomic nuclei, especially those of light nuclei, show strong α clustering, and many different types of α-cluster structure appear as the excitation energy increases [1][2][3][4][5]. In particular, the linear-chain configuration of three α particles (three linearly aligned α particles) suggested by Morinaga [6] has long been an important and interesting subject because of its exotic structure and large deformation, equivalent to hyperdeformation.…”

Section: Introductionmentioning

confidence: 99%

3αclustering in excited states ofC16

2014

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The α-cluster states of 16 C are investigated by using antisymmetrized molecular dynamics. It is shown that two different types of α-cluster states exist: triangular and linear-chain states. The former has an approximate isosceles triangular configuration of α particles surrounded by four valence neutrons occupying the sd shell, while the latter has the linearly aligned α particles with (sd) 2 (pf ) 2 neutrons. It is found that the structure of the linear-chain state is qualitatively understood in terms of the 3/2 − π and 1/2 − σ molecular orbits as predicted by molecular-orbital model, but there exists a non-negligible 10 Be + α + 2n correlation. The bandhead energies of the triangular and linear-chain rotational bands are 8.0 and 15.5 MeV, and the latter is close to the 4 He + 12 Be and 6 He + 10 Be threshold energies. It is also shown that the linear-chain state becomes the yrast state at J π = 10 + with E x = 27.8 MeV owing to its very large moment of inertia comparable with hyperdeformation.

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“…Summary and conclusion In this paper we have discussed the interrelation of the fundamental nuclear structure models, the shell, collective and cluster models from the viewpoint of symmetries. These models are based on different physical pictures, and their connection was established first in terms of the SU(3) symmetry for a single shell problem [1,2,3]. We have considered here the generalization of this relation along the major shell excitations.…”

Section: Intersectionmentioning

confidence: 99%

“…Elliott [1] showed how the quadrupole deformation and collective rotation can be derived from the spherical shell model: the states belonging to a collective band are determined by their specific SU(3) symmetry. Wildermuth and Kanellopoulos [2] established the relation between the shell and cluster models. They proved that the Hamiltonians of the two models can be rewritten into each other exactly in the harmonic oscillator approximation.…”

Section: Introductionmentioning

confidence: 99%

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On the relation of the shell, collective and cluster models

Cseh

2015

J. Phys.: Conf. Ser.

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Abstract. The intersection of the shell, collective and cluster models is described for multimajor-shell problems. IntroductionThe fundamental models of nuclear structure are based on different physical pictures. The shell model indicates that the atomic nucleus is something like a small atom, the cluster model suggests that it is similar to a molecule, while the collective model says that it is a microscopic liquid drop. Therefore, in order to understand the nuclear structure we need to study (among others) the interrelation of these models, find their common intersection, etc.The basic connections were found in the fifties. Elliott [1] showed how the quadrupole deformation and collective rotation can be derived from the spherical shell model: the states belonging to a collective band are determined by their specific SU(3) symmetry. Wildermuth and Kanellopoulos [2] established the relation between the shell and cluster models. They proved that the Hamiltonians of the two models can be rewritten into each other exactly in the harmonic oscillator approximation. This relation results in a close connection between the corresponding eigenvectors, too: the wavefunction of one model is a linear combination of those of the other, which belong to the same energy. Later on this relation was interpreted by Bayman and Bohr [3] in terms of the SU(3) symmetry. As a consequence, the cluster states are also selected from the shell model space by their specific SU(3) symmetries. (In fact only one kind of cluster states have this feature, and there are other kinds, too, as discussed later.)We will refer to this interrelation among the three basic structure models as the SU(3) connection. It was established in 1958 for a single major shell problem. Here we consider its extension to multi-major-shells.The connection of the shell model and the cluster model is especially interesting due to the fact that both models have a complete set of basis states, i.e. any nuclear states can be expanded in both bases. Depending on the simple or complicated nature of these expansions we can distinguish four different cases. i) If it is simple in the shell basis, but complicated in the cluster one, then we can speak about a simple shell state, which is a poor cluster state. ii) If it is simple in the cluster basis, but complicated in the shell basis, one has a good cluster state, which is a poor shell state. (Later on we will refer to these states as rigid molecule-like cluster

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The “cluster model” of the atomic nuclei

Cited by 265 publications

References 20 publications

Extreme quadrupole deformation and clusterization

Extreme quadrupole deformation and clusterization

3αclustering in excited states ofC16

On the relation of the shell, collective and cluster models

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