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Register a new userSymmetries and order in cluster nuclei
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Authors
Roelof Bijker
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It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and a regular tetrahedron for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles. Finally, some first results are presented for odd-cluster nuclei.
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The role of discrete (or point-group) symmetries is discussed in the framework of the Cluster Shell Model which describes the splitting of single-particle levels in the deformed field of cluster potentials. We discuss the classification of the eigenstates for the cases of a triangular and tetrahedral configuration of alpha-particles in terms of the irreducible representations of the double point groups D(3h) and T(d), respectively, and show how the discrete symmetry of a given eigenstate can be determined. Finally, we derive the Coriolis coupling for each one of these geometrical configurations.
In this contribution, we present evidence for the occurrence of triangular symmetry in cluster nuclei. We discuss the structure of rotational bands for 3-alpha and 3-alpha+1 configurations with triangular D(3h) symmetry by exploiting the double group D(3h), and study the application to 12C and 13C. The structure of rotational bands can be used as a fingerprint of the underlying geometric configuration of alpha-particles.
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 alpha-particles and within the framework of the cluster shell model (CSM) for nuclei composed of k alpha-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 8Be (k=2), 12C (k=3) and 16O (k=4), respectively, and for the associated double groups Z_2 and D_{3h} in the odd nuclei 9Be, 9B (k=2, x=1) and 13C (k=3, x=1), respectively.
In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three alpha-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13C.
First order quantum phase transition (QPT) between spherical and axially deformed nuclei shows coexisting, but well-separated regions of regular and chaotic dynamics. We employ a Hamiltonian of the Arima-Iachello Interacting Boson Model (IBM) with an arbitrarily high potential barrier separating the phases. Classical and quantum analyses reveal markedly distinct behavior of the two phases: Deformed phase is completely regular, while the spherical phase shows highly chaotic dynamics, similar to the Henon-Heiles system. Rotational bands with quasi-SU(3) characteristics built upon the regular vibrational spectrum of beta- and gamma-vibrations are observed in the deformed phase up to very high excitation energies.
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