Role of Symmetries in Nuclear Physics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 6019

Special Issue Editor


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Guest Editor
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico
Interests: symmetry in physics in general: nuclear physics, particle physics, general relativity; nuclear mathematical physics and nuclear models: construction of a useful basis using group theory, developing group theoretical methods for applications in nuclear and particle physics, developing nuclear models (geometric and algebraic ones); particle physics, related to the development of non-perturbative methods applied to low energy QCD; general relativity and possible extensions

Special Issue Information

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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Keywords

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

Published Papers (7 papers)

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Research

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16 pages, 1048 KiB  
Article
On the Breaking of the U(1) Peccei–Quinn Symmetry and Its Implications for Neutrino and Dark Matter Physics
by Osvaldo Civitarese
Symmetry 2024, 16(3), 364; https://doi.org/10.3390/sym16030364 - 18 Mar 2024
Viewed by 532
Abstract
The Standard Model of electroweak interactions is based on the fundamental SU(2)weak × U(1)elect representation. It assumes massless neutrinos and purely left-handed massive W± and Z0 bosons to which one should add the massless photon. The existence, [...] Read more.
The Standard Model of electroweak interactions is based on the fundamental SU(2)weak × U(1)elect representation. It assumes massless neutrinos and purely left-handed massive W± and Z0 bosons to which one should add the massless photon. The existence, verified experimentally, of neutrino oscillations poses a challenge to this scheme, since the oscillations take place between at least three massive neutrinos belonging to a mass hierarchy still to be determined. One should also take into account the possible existence of sterile neutrino species. In a somehow different context, the fundamental nature of the strong interaction component of the forces in nature is described by the, until now, extremely successful representation based on the SU(3)strong group which, together with the confining rule, give a description of massive hadrons in terms of quarks and gluons. To this is added the minimal U(1) Higgs group to give mass to the otherwise massless generators. This representation may also be challenged by the existence of both dark matter and dark energy, of still unknown composition. In this note, we shall discuss a possible connection between these questions, namely the need to extend the SU(3)strong × SU(2)weak × U(1)elect to account for massive neutrinos and dark matter. The main point of it is related to the role of axions, as postulated by Roberto Peccei and Helen Quinn. The existence of neutral pseudo-scalar bosons, that is, the axions, has been proposed long ago by Peccei and Quinn to explain the suppression of the electric dipole moment of the neutron. The associated U(1)PQ symmetry breaks at very high energy, and it guarantees that the interaction of other particles with axions is very weak. We shall review the axion properties in connection with the apparently different contexts of neutrino and dark matter physics. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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14 pages, 4499 KiB  
Article
Symmetries in Collisions as Explored through the Harmonic Oscillator
by Martin Freer and Miriam Davies
Symmetry 2024, 16(2), 231; https://doi.org/10.3390/sym16020231 - 14 Feb 2024
Viewed by 650
Abstract
The present study explores the symmetries associated with the cluster structure of light nuclei and draws the connection between solutions of the Schrödinger equation for the harmonic oscillator and the quasi-crystalline arrangements of α-particles, which gives rise to a series of collective behaviors. [...] Read more.
The present study explores the symmetries associated with the cluster structure of light nuclei and draws the connection between solutions of the Schrödinger equation for the harmonic oscillator and the quasi-crystalline arrangements of α-particles, which gives rise to a series of collective behaviors. The double-center harmonic oscillator is used to formulate the collisions of two nuclei described by harmonic oscillator solutions and traces out the evolution of the cluster structure in the dynamics of the collision process and demonstrates that the symmetries are preserved in this process. The connection between this study and stellar nucleosynthesis is described. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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13 pages, 1862 KiB  
Article
Moment of Inertia and Dynamical Symmetry
by József Cseh and Gábor Riczu
Symmetry 2023, 15(12), 2116; https://doi.org/10.3390/sym15122116 - 27 Nov 2023
Cited by 1 | Viewed by 649
Abstract
We investigate how the moment of inertia of the atomic nucleus can be calculated in terms of the invariant operator of its SU(3) symmetry. This question is important for model Hamiltonians containing the moment of inertia explicitly, e.g., those with multichannel dynamical symmetry, [...] Read more.
We investigate how the moment of inertia of the atomic nucleus can be calculated in terms of the invariant operator of its SU(3) symmetry. This question is important for model Hamiltonians containing the moment of inertia explicitly, e.g., those with multichannel dynamical symmetry, which describes many different bands in a unified way. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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15 pages, 1167 KiB  
Article
Gamow–Teller Beta Decay and Pseudo-SU(4) Symmetry
by Piet Van Isacker, Alejandro Algora, András Vitéz-Sveiczer, Gábor Gyula Kiss, Sonja Elena Agata Orrigo, Berta Rubio and Pablo Aguilera
Symmetry 2023, 15(11), 2001; https://doi.org/10.3390/sym15112001 - 31 Oct 2023
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Abstract
We report on recent experimental results on β decay into self-conjugate (N=Z) nuclei with mass number 58A70. Super-allowed β decays from the Jπ=0+ ground state of a [...] Read more.
We report on recent experimental results on β decay into self-conjugate (N=Z) nuclei with mass number 58A70. Super-allowed β decays from the Jπ=0+ ground state of a 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 58A70, 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 of pseudo-SU(4) symmetry for A=70. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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18 pages, 379 KiB  
Article
The Power of Symmetries in Nuclear Structure and Some of Its Problems
by Peter O. Hess
Symmetry 2023, 15(6), 1197; https://doi.org/10.3390/sym15061197 - 02 Jun 2023
Cited by 1 | Viewed by 966
Abstract
A review of several classical, algebraic models in nuclear structure physics, which use symmetries as an important tool, are presented. After a conceptual introduction to group theory, a selection of models is chosen to illustrate the methods and the power of the usage [...] Read more.
A review of several classical, algebraic models in nuclear structure physics, which use symmetries as an important tool, are presented. After a conceptual introduction to group theory, a selection of models is chosen to illustrate the methods and the power of the usage of symmetries. This enables us to describe very involved systems in a greatly simplified manner. Some problems are also discussed, when ignoring basic principles of nature, such as the Pauli exclusion principle. We also show that occasionally one can rescue these omissions. In a couple of representative models, applications of symmetries are explicitly applied in order to illustrate how extremely complicated systems can be treated. This contribution is meant as a review of the use of algebraic models in nuclear physics, leading to a better understanding of the articles in the same special volume. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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Review

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19 pages, 589 KiB  
Review
Nuclear Shape-Phase Transitions and the Sextic Oscillator
by Géza Lévai and José M. Arias
Symmetry 2023, 15(11), 2059; https://doi.org/10.3390/sym15112059 - 14 Nov 2023
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Abstract
This review delves into the utilization of a sextic oscillator within the β degree of freedom of the Bohr Hamiltonian to elucidate critical-point solutions in nuclei, with a specific emphasis on the critical point associated with the β shape variable, governing transitions from [...] Read more.
This review delves into the utilization of a sextic oscillator within the β degree of freedom of the Bohr Hamiltonian to elucidate critical-point solutions in nuclei, with a specific emphasis on the critical point associated with the β shape variable, governing transitions from spherical to deformed nuclei. To commence, an overview is presented for critical-point solutions E(5), X(5), X(3), Z(5), and Z(4). These symmetries, encapsulated in simple models, all model the β degree of freedom using an infinite square-well (ISW) potential. They are particularly useful for dissecting phase transitions from spherical to deformed nuclear shapes. The distinguishing factor among these models lies in their treatment of the γ degree of freedom. These models are rooted in a geometrical context, employing the Bohr Hamiltonian. The review then continues with the analysis of the same critical solutions but with the adoption of a sextic potential in place of the ISW potential within the β degree of freedom. The sextic oscillator, being quasi-exactly solvable (QES), allows for the derivation of exact solutions for the lower part of the energy spectrum. The outcomes of this analysis are examined in detail. Additionally, various versions of the sextic potential, while not exactly solvable, can still be tackled numerically, offering a means to establish benchmarks for criticality in the transitional path from spherical to deformed shapes. This review extends its scope to encompass related papers published in the field in the past 20 years, contributing to a comprehensive understanding of critical-point symmetries in nuclear physics. To facilitate this understanding, a map depicting the different regions of the nuclide chart where these models have been applied is provided, serving as a concise summary of their applications and implications in the realm of nuclear structure. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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16 pages, 1120 KiB  
Review
Spherical, Axial, and Triaxial Symmetries in the Study of Halo Nuclei with Covariant Density Functional Theory
by Yifeng Xiang, Qingjin Luo, Siqi Yang and Kaiyuan Zhang
Symmetry 2023, 15(7), 1420; https://doi.org/10.3390/sym15071420 - 14 Jul 2023
Cited by 1 | Viewed by 1088
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 [...] Read more.
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 spherical symmetry, the relativistic continuum Hartree–Bogoliubov theory describes the first halo nucleus 11Li self-consistently and predicts the giant halo phenomenon. Based on axial symmetry, the deformed relativistic Hartree–Bogoliubov theory in continuum has predicted axially deformed halo nuclei 42,44Mg and the shape decoupling effects therein. Based on triaxial symmetry, recently the triaxial relativistic Hartree–Bogoliubov theory in continuum has been developed and applied to explore halos in triaxially deformed nuclei. The theoretical frameworks of these models are presented, with the efficacy of exploiting symmetries highlighted. Selected applications to spherical, axially deformed, and triaxially deformed halo nuclei are introduced. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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