Dear Colleagues,

For many decades (starting with H. Weyl), symmetry (group theory) has played a central role in understanding complicated systems, such as the internal structure of nuclei. The use of symmetry has provided us with a powerful tool to develop models describing the involved spectra of nuclei and nuclear molecules in general, providing insight into the cluster structure of nuclei.

One aim of this Special Issue is to resume the achievements of the use of symmetry in nuclear physics, and the second aim is to provide information on the current and future developments of the use of symmetry in nuclear physics. The objective is to provide to a general audience a concise and complete compilation of what has been and will be achieved through the exploitation of symmetry.

The topics include the revision of algebraic models, such as the IBA with all its variants; microscopic, semi-microscopic and phenomenological cluster models using algebraic techniques; the restoration of symmetries in non-perturbative techniques such as BCS, TD and RPA; symmetry adapted basis, such as the SU(3) shell model and its derivatives; etc.

It is also hoped that the contributions will generate discussions on the latest research and the most recent developments in the application of symmetries to nuclear physics, as well as proposals regarding future developments. We may also consider contributions regarding the application of nuclear physics to the field of particle physics.

Prof. Dr. Peter Otto Hess
Guest Editor

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• role of symmetries
• nuclear structure models
• algebraic models
• cluster models
• symmetry adapted basis
• group theory

Title: SU(3) in nuclei: varietas delectat
Authors: Cseh, József
Affiliation: Atommagkutató Intéze Hungary
Abstract: Symmetries appear in atomic nuclei in a large variety. They can be exact or broken, simple and composite, be valid in general, or restricted to specific models. The SU(3) symmetry is especially popular since its invention by Elliott in 1958. In this paper we plan to give a brief review of its many different roles from a bird's eye view.

Title: Gamow-Teller beta decay and pseudo-SU(4) symmetry
Authors: P. Van Isacker, A. Algora, A. Vitéz-Sveiczer, G. Kiss, S. E. A. Orrigo, et al.
Affiliation: 1 Grand Accélérateur National d’Ions Lourds, Caen 2 Instituto de Fisica Corpuscular, Paterna 3 Institute for Nuclear Research (Atomki), Debrecen 4 PhD School of Physics, University of Debrecen
Abstract: Abstract: We report on recent experimental results for the β decay into self-conjugate (N = Z) nuclei with mass number 58 ≤ A ≤ 70. Super-allowed β decays from the Jπ = 0+ ground state of the Z = N + 2 parent nucleus are to the isobaric analogue state, through so-called Fermi transitions, and to Jπ = 1+ states, by way of Gamow–Teller (GT) transitions. The operator of the latter decay is a generator of Wigner’s SU(4) algebra and as a consequence GT transitions obey selection rules associated with this symmetry. Since SU(4) is progressively broken with increasing A, mainly as a consequence of the spin–orbit interaction, this symmetry is not relevant for the nuclei considered here. We argue, however, that the pseudo-spin–orbit splitting can be small in nuclei with 58 ≤ A ≤ 70, in which case nuclear states exhibit an approximate pseudo-SU(4) symmetry. To test this conjecture, GT decay strength is calculated with use of a schematic Hamiltonian with pseudo-SU(4) symmetry. Some generic features of the GT β decay due to pseudo-SU(4) symmetry are pointed out. The experimentally observed GT strength indicates a restoration pseudo-SU(4) symmetry for A = 70. Keywords: Gamow–Teller β decay; pseudo-SU(4) symmetry; odd–odd N = Z nuclei

Title: Spherical, axial, triaxial symmetries in the study of halo nuclei with covariant density functional theory
Authors: Kaiyuan Zhang
Affiliation: Institute of Nuclear Physics and Chemistry, CAEP, Mianyang, Sichuan 621900, China
Abstract: The halo phenomenon in exotic nuclei has long been an important frontier in nuclear physics research since its discovery in 1985. In parallel with the experimental progress in exploring halo nuclei, the covariant density functional theory has become one of the most successful tools for the microscopic study of halo nuclei. Based on the spherical symmetry, the relativistic continuum Hartree-Bogoliubov theory describes the first halo nucleus 11Li self-consistently and predicts the giant halo phenomenon. Based on the axial symmetry, the deformed relativistic Hartree-Bogoliubov theory in continuum has achieved great success, over the past dozen years, in studying deformed halo nuclei such as 17B, 22C, and 39Na. Based on the triaxial symmetry, recently the triaxial relativistic Hartree-Bogoliubov theory in continuum is developed and applied to explore halos in triaxial nuclei. The theoretical frameworks of these models are presented, where the power of the usage of symmetries is illustrated. Selected applications to halo nuclei are introduced.