Symmetry in Nuclear Physics: Model Calculations, Advances and Applications

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

Deadline for manuscript submissions: closed (15 March 2024) | Viewed by 19580

Special Issue Editors


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Guest Editor
Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, USA
Interests: nuclear structure; nuclear physics; algebra; nuclear astrophysics; neutrons
1. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, USA
2. Department of Physics, Liaoning Normal University, Dalian 116029, China
Interests: nuclear physics; quantum physics; theoretical physics

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Guest Editor
Institute of Nuclear and Particle Physics, National Centre for Scientific Research “Demokritos”, Athens, Greece
Interests: nuclear physics; theory of nuclear structure

Special Issue Information

Dear Colleagues,

Symmetry concepts have and are continuing to play very important roles in revealing simple patterns emerging in quantum many-body systems and providing well-organized descriptions for achieving a deeper understanding of the underlying physics. Examples include Wigner’s SU(4) spin-isospin symmetry, the SU(3) symmetry revealed in nuclear shell model through the pioneering work of Elliott, and Racah’s SU(2) quasi-spin for pairing are classic examples of the use of symmetry concepts in nuclei. Various associated Lie algebraic symmetries and their extensions within nuclear shell-model calculations continue to play a major role in helping to understanding nuclear structure physics. For example, the recent advancements that incorporate multi-shell excitations based on the Sp(3,R)⊃SU(3) symmetry opens up a new and pathway for managing shell model calculations that include open-shell considerations. Meanwhile, the interacting boson model (IBM) proposed by Arima and Iachello in the late seventies describes the collective excitations in even-even nuclei with simplicity based on the U(6) symmetry of S and D nucleon pairs approximated as bosons, which can also be extended to describe odd mass and odd-odd nuclei by including single valence proton and/or neutron degrees of freedom resulting in the interacting boson-fermion model (IBFM). Multi-shell extensions with 2n-particle and 2n-hole configuration mixing in both the IBM and the IBFM have also been met with good success in elucidating intruder states and in understanding shape coexistence phenomena.

This special issue focuses on recent original research that exploit symmetries in atomic nuclei ranging from the use of and innovatiions to various versions of the shell model as well as for the interacting boson, and including–as deemed to be appropriate–various mixed boson-fermion coupling modes. In addition, short review articles are also encouraged that seek to advance a bridging of the gap between low-energy (MeV scale) nuclear structure studies and high-energy (GeV scale) studies of hadronic matter, especially as the latter may seek to probe the intersection of the Shell Model and the Standard Model.

Prof. Dr. Jerry Paul Draayer
Dr. Feng Pan
Dr. Andriana Martinou
Guest Editors

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Keywords

  • nuclear structure and reactions
  • shell model
  • the interacting boson and boson-fermion model
  • symmetries in atomic nuclei and hadronic systems

Published Papers (7 papers)

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Research

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12 pages, 783 KiB  
Article
Correlation of Neutrinoless Double-β Decay Nuclear Matrix Element with E2 Strength
by Changfeng Jiao, Cenxi Yuan and Jiangming Yao
Symmetry 2023, 15(2), 552; https://doi.org/10.3390/sym15020552 - 19 Feb 2023
Cited by 1 | Viewed by 1057
Abstract
We explore the correlation of the neutrinoless double-β decay nuclear matrix element (NME) with electric quadrupole (E2) strength in the framework of the Hamiltonian-based generator-coordinate method, which is a configuration-mixing calculation of symmetry-restored intrinsic basis states. The restoration of symmetries [...] Read more.
We explore the correlation of the neutrinoless double-β decay nuclear matrix element (NME) with electric quadrupole (E2) strength in the framework of the Hamiltonian-based generator-coordinate method, which is a configuration-mixing calculation of symmetry-restored intrinsic basis states. The restoration of symmetries that are simultaneously broken in the mean-field states allows us to compute the structural and decay properties associated with wave functions characterized by good quantum numbers. Our calculations show a clear anti-correlation between the neutrinoless double-β decay NME and the transition rate of the collective quadrupole excitation from the ground state in response to artificial changes of the quadrupole–quadrupole interaction. The anti-correlation is more remarkable in the decay from a weakly deformed parent nucleus to a more deformed grand-daughter nucleus. This interrelation may provide a way to reduce the uncertainty of the nuclear matrix element. Full article
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25 pages, 525 KiB  
Article
The Role of the Hidden Color Channel in Some Interesting Dibaryon Candidates
by Lianrong Dai, Yuhang Wang, Langning Chen and Tiange Zhang
Symmetry 2023, 15(2), 446; https://doi.org/10.3390/sym15020446 - 07 Feb 2023
Viewed by 1419
Abstract
Nowadays, exploring dibaryon candidates has attracted much attention, both theoretically and experimentally. It is important to find a reasonable model to predict the possible dibaryon candidates. The chiral SU(3) quark model is just one of the most successful models, with which we can [...] Read more.
Nowadays, exploring dibaryon candidates has attracted much attention, both theoretically and experimentally. It is important to find a reasonable model to predict the possible dibaryon candidates. The chiral SU(3) quark model is just one of the most successful models, with which we can reasonably explain the experimental binding energies of baryon’s ground state and the properties of deuteron, NN and YN scattering processes. By utilizing the same set of model parameters, we predicted the nonstrange d* dibaryon with a binding energy of 84MeV, which is consistent with a recent experiment in which we also found that the hidden color (CC) channel plays an important role in forming this bound state. Due to the theoretical investigation of the CC channel being scarce for dibaryons, we explore other possible and interesting dibaryon candidates in the present work. According to the symmetry properties, we chose six interesting candidates, including strangeness 0,1,5,6 systems. All the hidden color wave functions were built, and the spin-flavor-color matrix elements were systematically evaluated. Then, we applied these obtained matrix elements to further dynamically solve the corresponding resonating group method’s equation in a coupled-channel calculation. The results show that the coupling to the CC channel plays an significant role in forming each spin S = 3 state, where tensor coupling is also included and has an obvious effect in forming each S = 0 state. The present work is significant in helping us to acquire deeper understanding of the effects of the hidden color channel and QCD phenomenology. Full article
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11 pages, 259 KiB  
Article
On the Logical Structure of Composite Symmetries in Atomic Nuclei
by József Cseh
Symmetry 2023, 15(2), 371; https://doi.org/10.3390/sym15020371 - 30 Jan 2023
Cited by 2 | Viewed by 969
Abstract
This investigation involves composite symmetries, which connect different components of atomic nuclei. In particular, supersymmetry (SUSY) connects boson and fermion sectors, and multiconfigurational symmetry (MUSY) bridges different configurations, such as shell, quartet, or cluster configurations. Both SUSY and MUSY contain a usual dynamical [...] Read more.
This investigation involves composite symmetries, which connect different components of atomic nuclei. In particular, supersymmetry (SUSY) connects boson and fermion sectors, and multiconfigurational symmetry (MUSY) bridges different configurations, such as shell, quartet, or cluster configurations. Both SUSY and MUSY contain a usual dynamical symmetry in each component, and further symmetry connects the components to each other. The varieties of the connecting symmetries and their logical structure are analyzed and compared. Full article
13 pages, 444 KiB  
Article
Stellar β Decay Rates for 63Co and 63Ni by the Projected Shell Model
by Zi-Rui Chen and Long-Jun Wang
Symmetry 2023, 15(2), 315; https://doi.org/10.3390/sym15020315 - 22 Jan 2023
Cited by 3 | Viewed by 1036
Abstract
β decay for 63Co-63Ni-63Cu region nuclei play important roles in core-collapse supernovae and the slow neutron-capture (s) process. In this work, the stellar β decay rates for 63Co and 63Ni are studied [...] Read more.
β decay for 63Co-63Ni-63Cu region nuclei play important roles in core-collapse supernovae and the slow neutron-capture (s) process. In this work, the stellar β decay rates for 63Co and 63Ni are studied within the projected shell model where the effects of thermally populated parent-nucleus excited states are analyzed. For 63Co, the calculated stellar β decay rates are lower than the results of the conventional shell model. For the s-process branching point 63Ni, the β decay rate under a terrestrial condition is well described, and the calculated stellar β decay rates in the s-process condition turn out to increase with stellar temperature due to the contribution from parent-nucleus excited states. Full article
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14 pages, 398 KiB  
Article
Hidden Euclidean Dynamical Symmetry in the U(n + 1) Vibron Model
by Yu Zhang, Zi-Tong Wang, Hong-Di Jiang and Xin Chen
Symmetry 2022, 14(10), 2219; https://doi.org/10.3390/sym14102219 - 21 Oct 2022
Cited by 4 | Viewed by 1080
Abstract
Based on the boson realization of the Euclidean algebras, it is found that the E(n) dynamical symmetry (DS) may emerge at the critical point of the U(n)-SO(n+1) quantum phase transition. To justify this finding, we [...] Read more.
Based on the boson realization of the Euclidean algebras, it is found that the E(n) dynamical symmetry (DS) may emerge at the critical point of the U(n)-SO(n+1) quantum phase transition. To justify this finding, we provide a detailed analysis of the transitional Hamiltonian in the U(n+1) vibron model in both quantal and classical ways. It is further shown that the low-lying structure of 82Kr can serve as an excellent empirical realization of the E(5) DS, which provides a specific example of the Euclidean DS in experiments. Full article
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Review

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57 pages, 854 KiB  
Review
Multiple Multi-Orbit Pairing Algebras in Nuclei
by Venkata Krishna Brahmam Kota and Rankanidhi Sahu
Symmetry 2023, 15(2), 497; https://doi.org/10.3390/sym15020497 - 13 Feb 2023
Cited by 1 | Viewed by 4901
Abstract
The algebraic group theory approach to pairing in nuclei is an old subject and yet it continues to be important in nuclear structure, giving new results. It is well known that for identical nucleons in the shell model approach with jj [...] Read more.
The algebraic group theory approach to pairing in nuclei is an old subject and yet it continues to be important in nuclear structure, giving new results. It is well known that for identical nucleons in the shell model approach with jj coupling, pairing algebra is SU(2) with a complementary number-conserving Sp(N) algebra and for nucleons with good isospin, it is SO(5) with a complementary number-conserving Sp(2Ω) algebra. Similarly, with LS coupling and isospin, the pairing algebra is SO(8). On the other hand, in the interacting boson models of nuclei, with identical bosons (IBM-1) the pairing algebra is SU(1, 1) with a complementary number-conserving SO(N) algebra and for the proton–neutron interacting boson model (IBM-2) with good F-spin, it is SO(3, 2) with a complementary number-conserving SOB) algebra. Furthermore, in IBM-3 and IBM-4 models several pairing algebras are possible. With more than one j or orbit in shell model, i.e., in the multi-orbit situation, the pairing algebras are not unique and we have the new paradigm of multiple pairing [SU(2), SO(5) and SO(8)] algebras in shell models and similarly there are multiple pairing algebras [SU(1, 1), SO(3, 2) etc.] in interacting boson models. A review of the results for multiple multi-orbit pairing algebras in shell models and interacting boson models is presented in this article with details given for multiple SU(2), SO(5), SU(1, 1) and SO(3, 2) pairing algebras. Some applications of these multiple pairing algebras are discussed. Finally, multiple SO(8) pairing algebras in shell model and pairing algebras in IBM-3 model are briefly discussed. Full article
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34 pages, 2488 KiB  
Review
The Proxy-SU(3) Symmetry in Atomic Nuclei
by Dennis Bonatsos, Andriana Martinou, Spyridon Kosmas Peroulis, Theodoros John Mertzimekis and Nikolay Minkov
Symmetry 2023, 15(1), 169; https://doi.org/10.3390/sym15010169 - 06 Jan 2023
Cited by 8 | Viewed by 6630
Abstract
The microscopic origins and the current predictions of the proxy-SU(3) symmetry model of atomic nuclei were reviewed. Beginning with experimental evidence for the special roles played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced; its validity is demonstrated [...] Read more.
The microscopic origins and the current predictions of the proxy-SU(3) symmetry model of atomic nuclei were reviewed. Beginning with experimental evidence for the special roles played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced; its validity is demonstrated through Nilsson model calculations and its connection to the spherical shell model. The major role played by the highest weight-irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables β and γ for even–even nuclei in the explanation of the dominance of prolate over oblate shapes in the ground states of even–even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, and in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined. Full article
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