The algebraic cluster model: Structure of 16O

Bijker, R.; Iachello, F.

doi:10.1016/j.nuclphysa.2016.08.008

Cited by 59 publications

(98 citation statements)

References 91 publications

(162 reference statements)

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“…An algebraic description of this configuration is given by the algebra of U (10) [40,41]. This algebra is constructed with boson creation…”

Section: Tetrahedral Configurationmentioning

confidence: 99%

“…States can be classified as This imposes some conditions on the allowed values of L which depend on t. A derivation of the allowed values is given in [41]. For the ground state, t = A, and for the fundamental vibrations with t = A, E and F of Fig.…”

Section: Tetrahedral Configurationmentioning

confidence: 99%

“…. , corresponding to the A 1 representation of the tetrahedral group, T d [41]. The charge and matter densities of a tetrahedral configuration are shown in Fig.…”

Section: Tetrahedral Configurationmentioning

confidence: 99%

“…The occurrence of T d symmetry in 16 O was emphasized by Robson [13,14] in the 1970s and more recently revisited in [40,41]. Energy levels have been analyzed with Eq.…”

Section: Tetrahedral 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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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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“…An algebraic description of this configuration is given by the algebra of U (10) [40,41]. This algebra is constructed with boson creation…”

Section: Tetrahedral Configurationmentioning

confidence: 99%

Section: Tetrahedral Configurationmentioning

confidence: 99%

“…. , corresponding to the A 1 representation of the tetrahedral group, T d [41]. The charge and matter densities of a tetrahedral configuration are shown in Fig.…”

Section: Tetrahedral Configurationmentioning

confidence: 99%

“…The occurrence of T d symmetry in 16 O was emphasized by Robson [13,14] in the 1970s and more recently revisited in [40,41]. Energy levels have been analyzed with Eq.…”

Section: Tetrahedral 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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“…It is well known that clusters, and especially alpha clusters, play a fundamental role in the nuclear structure of light nuclei (for a review see [5]). For example, 8 Be only exists as a resonant L = 0 state of two alpha particles that can even rotate up to L = 4 around a common center of mass. Nuclei and the nucleons that move inside them are most certainly not rigid systems as the chemical molecules, nonetheless it is very profitable to apply the language and the methods of quantum chemistry to nuclear systems, because some light nuclei, or maybe only a part of their spectrum, can be described as a sort of soft nuclear molecule, in which the clusters (that take the place of the atoms) perform large amplitude fluctuations around the equilibrium points, the mean value of kinetic energy of these subsystem being very large and comparable with typical nuclear excitation energies.…”

Section: Clustering In Nuclei and Nuclear Moleculesmentioning

confidence: 99%

How to determine the shape of nuclear molecules with polarized gamma-rays

Fortunato

2020

SciPost Phys. Proc.

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A method has been recently proposed to establish the geometry of the alpha-cluster arrangement in 12 C making use of polarized gamma-rays. The ratio of intensities of scattered radiation at 90 degrees along and perpendicular to the initial direction of the electric field vector, called depolarization ratio, is a key quantity that allows to underpin the nature of totally symmetric modes of vibrations. This allows to connect with the underlying pointgroup structure and therefore to the geometric shape of the nuclear molecule. This method is reviewed for 12 C and extended to other configurations, such as three unequal clusters and four identical clusters (e.g. 16 O).

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Clusters in light nuclei: history and recent developments

Lombardo,

Dell’Aquila

2023

Riv. Nuovo Cim.

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In this review, we discuss recent advancements in the study of clustering phenomena occurring in light nuclei, and their influence on nuclear structure, dynamics, and astrophysics. In the introduction, we outline the historical steps leading to the concept of $$\alpha $$ α -clusterization in nuclei and provide a comprehensive description of the evolution of nuclear models capable to describe clustering aspects in nuclear systems and of the main experiments and discoveries leading to the development of this research field. We also describe some spectroscopic techniques that are used to establish the clustered nature of a given nuclear state. Some relevant experimental and theoretical findings recently reported both in experimental and theoretical works are discussed in the text. We put emphasis on recent achievements and remaining problems in the description of the structure of light isotopes, from helium to neon, including both self- and non-self-conjugate nuclei. Particular attention to the implication in the nuclear astrophysics context and to clustering effects in the dynamics of nuclear reactions is pursued all along the review.

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The algebraic cluster model: Structure of 16O

Cited by 59 publications

References 91 publications

Cluster structure of light nuclei

Cluster structure of light nuclei

How to determine the shape of nuclear molecules with polarized gamma-rays

Clusters in light nuclei: history and recent developments

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