Geometrical symmetries of nuclear systems: ${{ \mathcal D }}_{3h}$ and ${{ \mathcal T }}_{d}$ symmetries in light nuclei

Bijker, R.

doi:10.1088/0031-8949/91/7/073005

Cited by 15 publications

(17 citation statements)

References 90 publications

(249 reference statements)

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“…Comparison between the theoretical and experimental[63] spectrum of 9 B. The observed level at 1.5 MeV is tentatively assigned as J P = 1/2 + and that at 4.8 MeV to 3/2 + in analogy with 9 Be.…”

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confidence: 87%

“….. We note here that the rotational bands for a triangular configuration are different from those of a dumbbell and of the collective model [64] since they include several values of K as given in Eq. (63).…”

Section: Equilateral Triangle Configurationmentioning

confidence: 99%

“…Comparison between the theoretical and experimental[63] spectrum of 9 Be. The dashed region is given by the width of the states.…”

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confidence: 99%

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Cluster structure of light nuclei

Bijker

Iachello

2020

Progress in Particle and Nuclear Physics

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We review recent studies of the cluster structure of light nuclei within the framework of the algebraic cluster model (ACM) for nuclei composed of k α-particles and within the framework of the cluster shell model (CSM) for nuclei composed of k α-particles plus x additional nucleons. The calculations, based on symmetry considerations and thus for the most part given in analytic form, are compared with experiments in light cluster nuclei. The comparison shows evidence for Z 2 , D 3h and T d symmetry in the even-even nuclei 8 Be (k = 2), 12 C (k = 3) and 16 O (k = 4), respectively, and for the associated double groups Z ′ 2 and D ′ 3h in the odd nuclei 9 Be, 9 B (k = 2, x = 1) and 13 C (k = 3, x = 1), respectively. configurations for nuclei composed of k α-particles, here referred as kα nuclei.In particular, the suggested configurations of the ground state were, for k = 2 a dumbbell configuration with Z 2 symmetry ( 8 Be), for k = 3 an equilateral triangle with D 3h symmetry ( 12 C) and for k = 4 a tetrahedron with T d symmetry ( 16 O), as shown in Fig. 1. Brink's suggestion stimulated a considerable amount of work in an attempt to derive cluster properties from the shell model, especially by the Japanese school [8][9][10][11] and from mean field theories [12]. Also, the cluster structure of specific nuclei was extensively investigated, as for example in 16 O [13,14], and Brink's model was applied to a wide range of cluster nuclei from 12 C to 44 Ti in [15,16]. A review of cluster models up to 2006 can be found in [17], and more recent ones in [18] and [19].In recent years, there has been considerable renewed interest in the structure of α-cluster nuclei, especially for the nucleus 12 C [20]. The observation of new rotational states built on the ground state [21-24] and the Hoyle state [25-27] has stimulated a large effort to understand the structure of 12 C ranging from studies based on Antisymmetric Molecular Dynamics (AMD) [28], Fermion Molecular Dynamics (FMD) [29], BEC-like cluster model [30], ab initio no-core shell model [31-33], lattice EFT [34-36], no-core symplectic model [37] and the Algebraic Cluster Model (ACM) [38][39][40][41]. In the first part of this paper, we review the ACM as applied to kα nuclei with k = 2, 3, 4.An important question is the extent to which cluster structures survive the addition of nucleons (protons and neutrons). We refer to nuclei composed of k α-particles plus x nucleons as kα + x nuclei. This question has also been addressed in the past, especially in the case of the Be isotopes seen as 8 Be + x nucleons, with a variety of methods [42][43][44][45][46][47] culminating, in the 1970's, in the extensive work of Okabe, Abe and Tanaka [48, 49] using the Linear Combination of Atomic Orbitals (LCAO) method and its generalizations. In recent years, FMD [50-53] and AMD [54-56] calculations have provided very detailed and accurate microscopic descriptions of the Be isotopes with large overlap with the Brink model [7]. In another seminal development, Von Oertzen [57-60] hasdiscussed the ...

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confidence: 87%

Section: Equilateral Triangle Configurationmentioning

confidence: 99%

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Cluster structure of light nuclei

Bijker

Iachello

2020

Progress in Particle and Nuclear Physics

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“…In practice, the wave functions are obtained numerically by diagonalization, and hence are determined up to a sign. The relative phases of the degenerate representations, the two-dimensional E, and the threedimensional F 2 and F 1 , can be determined from the off-diagonal matrix elements of P (1234) [51].…”

Section: Permutation Symmetrymentioning

confidence: 99%

“…A preliminary account of part of this work has appeared in Refs. [32,49,50,51]. Here we develop the U (10) ACM in more detail, and especially we present a detailed analysis of the spectroscopic properties of 16 O including energies, transition rates and electromagnetic form factors, and show that 16 O can be, to a good approximation, described by a 4α configuration with T d symmetry.…”

Section: Introductionmentioning

confidence: 97%

The algebraic cluster model: Structure of 16O

Bijker

Iachello

2017

Nuclear Physics A

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We discuss an algebraic treatment of four-body clusters which includes both continuous and discrete symmetries. In particular, tetrahedral configurations with T d symmetry are analyzed with respect to the energy spectrum, transition form factors and B(EL) values. It is concluded that the low-lying spectrum of 16 O can be described by four α particles at the vertices of a regular tetrahedron, not as a rigid structure but rather a more floppy structure with relatively large rotation-vibration interactions and Coriolis forces.

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Alpha particle clusters and their condensation in nuclear systems

et al. 2016

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In this article we review the present status of α clustering in nuclear systems. An important aspect is first of all condensation in nuclear matter. Like for pairing, quartetting in matter is at the root of similar phenomena in finite nuclei. Cluster approaches for finite nuclei are shortly recapitulated in historical order. The α container model as recently been proposed by Tohsaki-Horiuchi-Schuck-Röpke (THSR) will be outlined and the ensuing condensate aspect of the Hoyle state at 7.65 MeV in 12 C investigated in some detail. A special case will be made with respect to the very accurate reproduction of the inelastic form factor from the ground to Hoyle state with the THSR description. The extended volume will be deduced. New developments concerning excitations of the Hoyle state will be discussed. After 15 years since the proposal of the α condensation concept a critical assessment of this idea will be given. Alpha gas states in other nuclei like 16 O and 13 C will be considered. An important aspect are experimental evidences, present and future ones.The THSR wave function can also describe configurations of one α particle on top of a doubly magic core. The cases of 20 Ne and 212 Po will be investigated.

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Geometrical symmetries of nuclear systems: ${{ \mathcal D }}_{3h}$ and ${{ \mathcal T }}_{d}$ symmetries in light nuclei

Cited by 15 publications

References 90 publications

Cluster structure of light nuclei

Cluster structure of light nuclei

The algebraic cluster model: Structure of 16O

Alpha particle clusters and their condensation in nuclear systems

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