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Open AccessArticle

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 694

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

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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Open AccessArticle

A U(6) Boson Model for Deformed Nuclei

by

Andriana Martinou

Symmetry 2023, 15(2), 455; https://doi.org/10.3390/sym15020455 - 08 Feb 2023

Viewed by 969

Abstract

The Interacting Boson Model is one of the most famous group-theoretical nuclear models, which established the use of the

U (6)

symmetry in nuclei, built upon the

s, d

bosons, which derive by nucleon pairs. In this article, it is [...] Read more.

The Interacting Boson Model is one of the most famous group-theoretical nuclear models, which established the use of the

U (6)

symmetry in nuclei, built upon the

s, d

bosons, which derive by nucleon pairs. In this article, it is suggested that the symmetric pairs of the valence harmonic oscillator quanta can be used approximately as the s and d bosons of a new

U (6)

Boson Model, applicable in medium mass and heavy nuclei. The main consequence of this interpretation is that the number of bosons is the number of the pairs of the valence harmonic oscillator quanta, which occur from the occupation of the Shell Model orbitals by nucleons. Full article

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

Open AccessArticle

The Role of the Hidden Color Channel in Some Interesting Dibaryon Candidates

by

,

,

and

Symmetry 2023, 15(2), 446; https://doi.org/10.3390/sym15020446 - 07 Feb 2023

Viewed by 1126

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

84 MeV

, 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

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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Open AccessArticle

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

Viewed by 679

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

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

Open AccessArticle

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 1 | Viewed by 705

Abstract

β^{-}

decay for

^{63}

Co-

^{63}

Ni-

^{63}

Cu 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

^{63}

Co and

^{63}

Ni are studied [...] Read more.

β^{-}

decay for

^{63}

Co-

^{63}

Ni-

^{63}

Cu 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

^{63}

Co and

^{63}

Ni are studied within the projected shell model where the effects of thermally populated parent-nucleus excited states are analyzed. For

^{63}

Co, the calculated stellar

β^{-}

decay rates are lower than the results of the conventional shell model. For the s-process branching point

^{63}

Ni, 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

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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Open AccessArticle

The Rotor-Vibrator Plus Multi-Particle-Hole Description of ¹⁵⁴Gd

by

,

,

,

and

Symmetry 2022, 14(12), 2620; https://doi.org/10.3390/sym14122620 - 10 Dec 2022

Viewed by 699

Abstract

Based on the well-known rotor-vibrator model and the particle-plus-rotor model, multi-particle-hole excitations from a collective even-even core described by the rotor-vibrator is considered to describe well-deformed even-even nuclei. Like the particle-plus-rotor model, the intrinsic Vierergruppe (D₂) symmetry is still preserved in [...] Read more.

Based on the well-known rotor-vibrator model and the particle-plus-rotor model, multi-particle-hole excitations from a collective even-even core described by the rotor-vibrator is considered to describe well-deformed even-even nuclei. Like the particle-plus-rotor model, the intrinsic Vierergruppe (D₂) symmetry is still preserved in the rotor-vibrator plus multi-particle-hole description. It is shown that a series of experimentally observed 0⁺ states in these nuclei may be interpreted as the multi-particle-hole excitations in a complementary manner to the beta and gamma vibrations described by the rotor-vibrator model. As a typical example of the model application, low-lying positive parity level energies below 1.990 MeV in the eight experimentally identified positive parity bands; a series of

0^{+}

excitation energies up to

0_{16}^{+}

; and some experimentally known B(E2) values, E2 branching ratios, and E2/M1 and E0/E2 mixing ratios of ¹⁵⁴Gd are fitted and compared to the experimental data. The results suggest that the multi-particle-hole-pair configuration mixing may play a role in these 0⁺ states. Full article

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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Open AccessArticle

Shape Phase Transitions in Even–Even ^176–198Pt: Higher-Order Interactions in the Interacting Boson Model

by

Dongkang Li

,

Tao Wang

and

Feng Pan

Symmetry 2022, 14(12), 2610; https://doi.org/10.3390/sym14122610 - 09 Dec 2022

Cited by 3 | Viewed by 856

Abstract

Dynamical symmetry plays a dominant role in the interacting boson model in elucidating nuclear structure, for which group theoretical or algebraic techniques are powerful. In this work, the higher-order interactions required in describing triaxial deformation in the interacting boson model are introduced to [...] Read more.

Dynamical symmetry plays a dominant role in the interacting boson model in elucidating nuclear structure, for which group theoretical or algebraic techniques are powerful. In this work, the higher-order interactions required in describing triaxial deformation in the interacting boson model are introduced to improve the fitting results to low-lying level energies,

B (E 2)

values and electric quadrupole moments of even–even nuclei. As an example of the model application, the low-lying excitation spectra and the electromagnetic transitional properties of even–even ^176−198Pt are fitted and compared to the experimental data and the results of the consistent-Q formalism. It is shown that the results obtained from the model are better than those of the original consistent-Q formalism, indicating the importance of the higher-order interactions in describing the structure and the shape phase evolution of these nuclei. Full article

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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Open AccessArticle

The Particle-Rotor-Quadrupole-Coupling Model for Transitional Odd-A Nuclei

by

,

,

,

,

and

Symmetry 2022, 14(12), 2578; https://doi.org/10.3390/sym14122578 - 06 Dec 2022

Viewed by 832

Abstract

The particle-rotor-quadrupole-coupling model, in which the quadrupole–quadrupole interaction of the even-even core is described by a triaxial rotor with a single-j particle, is adopted to describe low-lying spectra of odd-A nuclei within the vibrational to triaxial transition region. In contrast to the [...] Read more.

The particle-rotor-quadrupole-coupling model, in which the quadrupole–quadrupole interaction of the even-even core is described by a triaxial rotor with a single-j particle, is adopted to describe low-lying spectra of odd-A nuclei within the vibrational to triaxial transition region. In contrast to the particle-plus-rotor-model, the quadrupole–quadrupole interaction introduced in the particle-rotor-quadrupole-coupling model keeps the rotational symmetry in the collective model framework without approximation. To demonstrate the usability, low-lying level energies, reduced E2 transition probabilities, and ground-state quadrupole moments of ¹³⁵Ba and ¹³¹Xe are fit by the model, of which the results are compared with the experimental data and those of other models. It is shown that the fitting results of the particle-rotor-quadrupole-coupling model to the low-lying level energies, reduced E2 transition probabilities, and ground-state electric quadrupole moments of ¹³⁵Ba and ¹³¹Xe are the best, of which the model parameters of the even-even core are determined by the triaxial rotor model in fitting the low-lying spectra of ¹³⁴Ba and ¹³⁰Xe. In comparison with the E(5/4) model results of ¹³⁵Ba, it is also shown that the quadrupole–quadrupole interaction of the even-even core with the single particle adopted can indeed reproduce the E(5/4) critical point behavior. The fitting quality of the reduced E2 transition probabilities among low-lying states by the particle-rotor-quadrupole-coupling model is also noticeably improved. Thus, it can be concluded that the particle-rotor-quadrupole-coupling model is suitable to describe low-lying properties of odd-A nuclei within the transitional region. Full article

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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Open AccessArticle

Hidden Euclidean Dynamical Symmetry in the U(n + 1) Vibron Model

by

,

,

and

Symmetry 2022, 14(10), 2219; https://doi.org/10.3390/sym14102219 - 21 Oct 2022

Cited by 4 | Viewed by 779

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

^{82}

Kr 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

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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Review

Jump to: Research

Open AccessReview

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 4656

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 j − j [...] 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 j − j 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 L − S 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

S O (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 SO(Ω^B) algebra. Furthermore, in IBM-3 and IBM-4 models several pairing algebras are possible. With more than one j or ℓ 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

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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Open AccessFeature PaperReview

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 6 | Viewed by 1155

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

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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