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

Deadline for manuscript submissions: closed (31 July 2022) | Viewed by 29525

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Special Issue Editors

Prof. Dr. Yu-Gang Ma

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Guest Editor

Institute of Modern Physics, Fudan University, Shanghai, China
Interests: experiment and phenomenology of radioactive nuclear beam physics; heavy ion physics

Prof. Dr. De-Qing Fang

E-Mail Website
Guest Editor

Institute of Modern Physics, Fudan University, Shanghai, China
Interests: experimental radioactive nuclear beam physics

Prof. Dr. Fu-Rong Xu

E-Mail Website
Guest Editor

Institute of Theoretical Nuclear Physics, Peking Unversity, Beijing, China
Interests: nuclear structure theory; nuclear force; ab initio many-body theory

Special Issue Information

Dear Colleagues,

There are about 250 stable isotopes of the 90 elements. Up to now, the number of radioactive isotopes produced in the laboratory is 3000~4000, and there may be 8000~10,000 as predicted by theory. Compared to the stable nuclei, new phenomena and new physics appear in the weakly bound nuclei far from the beta-stability line. It becomes a challenge to explain the exotic phenomena for the traditional nuclear theory built on the properties of stable nuclei. Thus, radioactive nuclear beam (RNB) physics has become one of the most important frontiers of nuclear science. Through systematic experimental and theoretical studies, the most important open questions in nuclear physics could be revealed and understood: the nuclear shell structure evolution with increasing isospin; clustering and halo structure; new forms of collective motion and shape coexistence in neutron-rich nuclei; the exotic radioactivity in nuclei close to the proton and neutron drip-line; the existence limit of nuclei; the synthesis of heavy elements and their influences on the properties of stars; etc.

Please note that all submitted papers must be within the general scope of the Symmetry journal.

Prof. Dr. Yu-Gang Ma
Prof. Dr. De-Qing Fang
Prof. Dr. Fu-Rong Xu
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

nuclear shell structure evolution
clustering and halo structure
new forms of collective motion and shape coexistence
isospin symmetry breaking
the exotic radioactivity in weakly bound nuclei
new isotopes and the neutron/proton drip line
the production and detection of unstable nuclei
synthesis of nuclei heavier than Fe and nuclear astrophysics
equation of state of asymmetric nuclear matter

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Published Papers (12 papers)

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Research

10 pages, 1902 KiB

Open AccessFeature PaperArticle

Nuclear Mass Predictions of the Relativistic Density Functional Theory with the Kernel Ridge Regression and the Application to r-Process Simulations

by Lihan Guo, Xinhui Wu and Pengwei Zhao

Symmetry 2022, 14(6), 1078; https://doi.org/10.3390/sym14061078 - 24 May 2022

Cited by 10 | Viewed by 3213

Abstract

The kernel ridge regression (KRR) and its updated version taking into account the odd-even effects (KRRoe) are employed to improve the mass predictions of the relativistic density functional theory. Both the KRR and KRRoe approaches can improve the mass predictions to a large extent. In particular, the KRRoe approach can significantly improve the predictions of the one-nucleon separation energies. The extrapolation performances of the KRR and KRRoe approaches to neutron-rich nuclei are examined, and the impacts of the KRRoe mass corrections on the r-process simulations are studied. It is found that the KRRoe mass corrections for the nuclei in the r-process path are remarkable in the light mass region, e.g.,

A < 150

, and this could influence the corresponding r-process abundances. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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10 pages, 599 KiB

Open AccessArticle

Study of α-Decay Energy by an Artificial Neural Network Considering Pairing and Shell Effects

by Hong-Qiang You, Zheng-Zhe Qu, Ren-Hang Wu, Hao-Ze Su and Xiao-Tao He

Symmetry 2022, 14(5), 1006; https://doi.org/10.3390/sym14051006 - 16 May 2022

Cited by 3 | Viewed by 1978

Abstract

We build and train an artificial neural network (ANN) model based on experimental

α

-decay energy (

Q_{α}

) data. In addition to decays between the ground states of parent and daughter nuclei, decays from the ground states of parent nuclei to [...] Read more.

We build and train an artificial neural network (ANN) model based on experimental

α

-decay energy (

Q_{α}

) data. In addition to decays between the ground states of parent and daughter nuclei, decays from the ground states of parent nuclei to the excited states of daughter nuclei are also included. In this way, the number of samples is increased dramatically. The

α

particle is assumed to have a spherical symmetric shape. The root-mean-square deviation between the calculated results obtained from the ANN model and the experimental data is 0.105 MeV. It shows a good predictive power for

α

-decay energy with the ANN model. The influence of different inputs is investigated. It is found that both the shell effect and the pairing effect result in an obvious improvement of the predictive power of the ANN model, and the shell effect plays a more important role. The optimal result can be obtained when both the shell and pairing effects are considered simultaneously. The application of the ANN model in predicting

α

-decay energy indicates a neutron magic number at

N = 184

in the superheavy nuclei mass region. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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11 pages, 431 KiB

Open AccessArticle

Nuclear Potentials Relevant to the Symmetry Energy in Chiral Models

by Niu Li, Si-Na Wei and Wei-Zhou Jiang

Symmetry 2022, 14(3), 474; https://doi.org/10.3390/sym14030474 - 26 Feb 2022

Cited by 3 | Viewed by 1725

Abstract

We employ the extended Nambu-Jona-Lasinio (NJL), linear-

σ

We employ the extended Nambu-Jona-Lasinio (NJL), linear-

σ

models, and the density-dependent model with chiral limits to work out the mean fields and relevant properties of nuclear matter. To have the constraint from the data, we re-examine the Dirac optical potentials and symmetry potential based on the relativistic impulse approximation (RIA). Unlike the extended NJL and the density-dependent models with the chiral limit in terms of the vanishing scalar density, the extended linear-

σ

model with a sluggish changing scalar field loses the chiral limit at the high-density end. The various scalar fields can characterize the different Schrödinger-equivalent potentials and kinetic symmetry energy in the whole density region and the symmetry potential in the intermediate density region. The drop in the scalar field due to the chiral restoration results in a clear rise of the kinetic symmetry energy. The chiral limit in the models gives rise to the softening of the symmetry potential and thereof the symmetry energy at high densities. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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13 pages, 6501 KiB

Open AccessArticle

The Flux Ratio of the [OIII]λλ5007,4959 Doublet with Redshift

by Mayalen A. Laker, Conner D. Camacho, Daniel Jones and Joseph Moody

Symmetry 2022, 14(2), 266; https://doi.org/10.3390/sym14020266 - 29 Jan 2022

Cited by 2 | Viewed by 3831

Abstract

As a test of the time symmetry of forbidden-line emission processes, we measured the [OIII]

λ λ

4959 and 5007 emission lines of more than 12,000 galaxies from the Sloan Digital Sky Survey DR8 to examine the [OIII]

λ λ

4959,5007 flux ratio [...] Read more.

As a test of the time symmetry of forbidden-line emission processes, we measured the [OIII]

λ λ

4959 and 5007 emission lines of more than 12,000 galaxies from the Sloan Digital Sky Survey DR8 to examine the [OIII]

λ λ

4959,5007 flux ratio as a function of redshift z. Using two different approaches, we fitted each line with a Gaussian curve and rejected any spectrum not conforming to requirements of line symmetry, S/N levels, and continuum fit. We found the variance in the ratio of flux to be between 4.7 and −3.3% for

0 < z < 0.433

which is consistent with no change. After correcting for systematic effects of noise, we found the mean value of the [OIII]

λ λ

4959,5007 flux ratio to be 2.98 ± 0.01 which is consistent with theory and previous studies using AGN spectra. We also used these data to estimate an upper limit on the time dependence of the fine structure constant

α

Δ α

α (0) < 1.4 \times 10^{- 5}

for galaxies within the same redshift range. This corresponds to

| α^{- 1} d α / d t | < 2 \times 10^{- 15}

^{- 1}

, which is also in line with previous estimates from SDSS QSO data. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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8 pages, 354 KiB

Open AccessArticle

Studies of Deformed Halo Structures of ³⁹Na and ⁴²Mg

by Qingzhen Chai, Hongxing Chen, Minghao Zha, Junchen Pei and Furong Xu

Symmetry 2022, 14(2), 215; https://doi.org/10.3390/sym14020215 - 23 Jan 2022

Cited by 2 | Viewed by 2475

Abstract

Background: The recent experimental discovery of drip-line nucleus ³⁹Na has attracted great interest in theoretical studies of exotic nuclear structures in this mass region. Methods: We solve the Skyrme–Hartree–Fock–Bogoliubov (Skyrme-HFB) equation within deformed coordinate-spaces. The present approach is suitable for descriptions of [...] Read more.

_{ext 1}^{*}

and UNEDF0

_{ext 1}

forces for Na and Mg isotopes close to the neutron drip line. The density distributions show that

^{39}

Na and

^{42}

Mg have deformed halo structures. Furthermore, there are significant influences of various pairing interactions on halo shapes at large distances. Conclusions: Both

^{39}

Na and

^{42}

Mg are very weakly bound with well prolate deformed cores. However, their surface halo structures are dependent on the choices of pairing interactions. The volume-type pairing interaction tends to predict a prolate deformed halo, while the halo deformations at large distances are reduced by adopting the surface pairing. We demonstrate that

^{39}

Na and

^{42}

Mg are promising candidates for two-neutron deformed halo nuclei. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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11 pages, 374 KiB

Open AccessArticle

Description for N = 126 Isotones ²¹⁰Po and ²¹²Rn with Particle-Hole Excited Nucleon-Pair Approximation and Realistic Effective Interaction

by Yi-Xing Wang, Yi-Yuan Cheng and Thomas T. S. Kuo

Symmetry 2022, 14(1), 181; https://doi.org/10.3390/sym14010181 - 17 Jan 2022

Viewed by 2204

Abstract

In this paper, we study yrast states of two

N = 126

isotones

^{210}

Po and

^{212}

Rn using the nucleon-pair approximation with particle–hole excitations and using a low-momentum interaction

V_{low - k}

renormalized from the free CD-Bonn

N N

potential. An [...] Read more.

In this paper, we study yrast states of two

N = 126

isotones

^{210}

Po and

^{212}

Rn using the nucleon-pair approximation with particle–hole excitations and using a low-momentum interaction

V_{low - k}

renormalized from the free CD-Bonn

N N

potential. An overall good agreement with experimental level structures,

B (E 2)

s, and

B (E 3)

s, is achieved. We also calculate the probabilities of neutron particle–hole excitations in these yrast states, with a focus on negative-parity states, which reflect the roles played by the neutron negative-parity configurations of one-particle-one-hole excitations across the

N = 126

shell gap and the negative-parity configurations of valence proton particles involving the

0 i_{13 / 2}

orbit. The

N = 126

shell gap is discussed in terms of energies of neutron one-particle-one-hole excitations. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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11 pages, 4959 KiB

Open AccessArticle

β-Delayed γ Emissions of ²⁶P and Its Mirror Asymmetry

by Hao Jian, Yufeng Gao, Fanchao Dai, Jiajian Liu, Xinxing Xu, Cenxi Yuan, Kazunari Kaneko, Yang Sun, Pengfei Liang, Guozhu Shi, Lijie Sun, Latsamy Xayavong, Chengjian Lin, Jenny Lee, Zhihuan Li, Yanyun Yang, Pengjie Li, Rui Fan, Sixian Zha, Haofan Zhu, Jinhai Li, Qirui Gao, Zhaozhan Zhang, Ruofu Chen, Jiansong Wang, Dongxi Wang, Hongyi Wu, Kang Wang, Yihua Lam, Fangfang Duan, Peng Ma, Zhihao Gao, Qiang Hu, Zhen Bai, Junbing Ma, Jianguo Wang, Fupeng Zhong, Chenguang Wu, Diwen Luo, Ying Jiang, Yang Liu, Dongsheng Hou, Ren Li, Nanru Ma, Weihu Ma, Gongming Yu, Dipika Patel, Shuya Jin, Yufeng Wang, Yuechao Yu, Qingwu Zhou, Peng Wang, Liyuan Hu, Xiang Wang, Hongliang Zang, Qingqing Zhao, Lei Yang, Peiwei Wen, Feng Yang, Huiming Jia, Gaolong Zhang, Min Pan, Xiaoyu Wang, Haohan Sun, Meng Wang, Zhengguo Hu, Xiaohong Zhou, Yuhu Zhang, Hushan Xu, Minliang Liu, Hooi-Jin Ong and Weiqing Yang Show full author list Hide full author list

Symmetry 2021, 13(12), 2278; https://doi.org/10.3390/sym13122278 - 30 Nov 2021

Cited by 7 | Viewed by 3050

Abstract

The study of the origin of asymmetries in mirror

β

decay is extremely important to understand the fundamental nuclear force and the nuclear structure. The experiment was performed at the National Laboratory of Heavy Ion Research Facility in Lanzhou (HIRFL) to measure the [...] Read more.

The study of the origin of asymmetries in mirror

β

β

-delayed

γ

rays of

^{26}

P by silicon array and Clover-type high-purity Germanium (HPGe) detectors. Combining with results from the

β

decay of

^{26}

P and its mirror nucleus

^{26}

Na, the mirror asymmetry parameter

δ

( ≡

f t^{+}

f t^{-}

− 1) was determined to be 46(13)% for the transition feeding the first excited state in the daughter nucleus. Our independent results support the conclusion that the large mirror asymmetry is close to the proton halo structure in

^{26}

P. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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10 pages, 656 KiB

Open AccessArticle

Nuclear Structure Evolution Reflected from Local Relations

by Man Bao and Qian Wei

Symmetry 2021, 13(12), 2253; https://doi.org/10.3390/sym13122253 - 26 Nov 2021

Cited by 2 | Viewed by 1703

Abstract

The structure evolution of nuclei which are in connection with symmetry breaking is one of the important problems not only for nuclear structures, but also for astrophysics and the spectroscopy of exotic nuclei. Many physical quantities can provide useful information of a shell [...] Read more.

N_{p} N_{n}

scheme respectively for the quadrupole deformation parameter and the excitation energy of the first

2^{+}

4^{+}

6^{+}

states, the

(α N^{'}_{n} + N^{'}_{p})

relation for nuclear charge radii and

α

decay energies, and the so-called “nonpairing” relation for binding energies and nuclear charge radii. All these relations reflect the evolution of nuclear structures, involving shells, subshells, shape coexistence, phase transition and the Wigner effect. Some results from different models can be verified with each other. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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8 pages, 595 KiB

Open AccessArticle

Effects of the Tensor Force on the Ground Properties of Zr Isotopes

by Chao-Feng Chen, Qi-Bo Chen, Xian-Rong Zhou and Yi-Yuan Cheng

Symmetry 2021, 13(11), 2193; https://doi.org/10.3390/sym13112193 - 17 Nov 2021

Cited by 2 | Viewed by 1492

Abstract

The effects of the tensor force on the ground properties of Zr isotopes are studied in the framework of the Skyrme–Hartree–Fock approach. It is found that the tensor force strongly affects the ground state energies and the geometric symmetry properties, in particular for [...] Read more.

N = 60

region. The effects are attributed to the fact that the tensor force enlarges the spin and pseudospin symmetry breaking and therefore results in a ∼2 MeV sub-shell gap between

d_{3 / 2}

and

s_{1 / 2}

single-particle levels. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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12 pages, 1422 KiB

Open AccessArticle

Quantifying the Effect of Initial Fluctuations on Isospin-Sensitive Observables from Heavy-Ion Collisions at Intermediate Energies

by Yongjia Wang, Zepeng Gao and Qingfeng Li

Symmetry 2021, 13(11), 2172; https://doi.org/10.3390/sym13112172 - 12 Nov 2021

Cited by 4 | Viewed by 1887

Abstract

Initial fluctuation is one of the ingredients that washes fingerprints of the nuclear symmetry energy on observables in heavy-ion collisions. By artificially using the same initial nuclei in all collision events, the effect of the initial fluctuation on isospin-sensitive observables, e.g., the yield [...] Read more.

N_{n}

N_{p}

^{3}

^{3}

He yield ratio, the yield ratio between charged pions

π^{-}

π^{+}

, and the elliptic flow ratio or difference between free neutrons and protons

v_{2}^{n}

v_{2}^{p}

(

v_{2}^{n}

v_{2}^{p}

), are studied within the ultrarelativistic quantum molecular dynamics (UrQMD) model. In practice, Au + Au collisions with impact parameter b = 5 fm and beam energy

E_{lab}

= 400 MeV/nucleon are calculated. It is found that the effect of the initialization on the yields of free protons and neutrons is small, while for the yield of pions, the directed and elliptic flows are found to be apparently influenced by the choice of initialization because of the strong memory effects. Regarding the isospin-sensitive observables, the effect of the initialization on

N_{n}

N_{p}

and

^{3}

^{3}

He is negligible, while

π^{-}

π^{+}

and

v_{2}^{n}

v_{2}^{p}

(

v_{2}^{n}

v_{2}^{p}

) display a distinct difference among different initializations. The fingerprints of symmetry energy on

π^{-}

π^{+}

and

v_{2}^{n}

v_{2}^{p}

can be either enhanced or reduced when different initializations are utilized. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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15 pages, 7234 KiB

Open AccessArticle

Cross-Shell Excitation in F and Ne Isotopes around N = 20

by Menglan Liu and Cenxi Yuan

Symmetry 2021, 13(11), 2167; https://doi.org/10.3390/sym13112167 - 12 Nov 2021

Cited by 3 | Viewed by 2082

Abstract

Within the framework of the configuration–interaction shell model, the present work applies three effective interactions to investigate the effects of the cross-shell excitation on F and Ne isotopes around N = 20, which are significantly proton–neutron asymmetric, and have different properties compared with the proton–neutron symmetric nuclei. It is shown that cross-shell excitation is necessary in order to reproduce separation energies, neutron drip lines, and low-energy levels of these isotopes. Furthermore, the cross-shell excitation of (0–5)ħω is suggested to be important in the description of ²⁹F and ³⁰Ne. However, the three interactions are insufficient in describing the bound structure of ^29,31Ne, and provide inconsistent shell structures and evolutions in the target nuclei. Their cross-shell interactions are suggested to be improved. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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19 pages, 498 KiB

Open AccessArticle

np-Pair Correlations in the Isovector Pairing Model

by Feng Pan, Yingwen He, Lianrong Dai, Chong Qi and Jerry P. Draayer

Symmetry 2021, 13(8), 1405; https://doi.org/10.3390/sym13081405 - 2 Aug 2021

Viewed by 2170

Abstract

A diagonalization scheme for the shell model mean-field plus isovector pairing Hamiltonian in the O(5) tensor product basis of the quasi-spin SU

_{Λ}

(2) ⊗ SU

_{I}

(2) chain is proposed. The advantage of the diagonalization scheme lies in the fact that not [...] Read more.

A diagonalization scheme for the shell model mean-field plus isovector pairing Hamiltonian in the O(5) tensor product basis of the quasi-spin SU

_{Λ}

(2) ⊗ SU

_{I}

(2) chain is proposed. The advantage of the diagonalization scheme lies in the fact that not only can the isospin-conserved, charge-independent isovector pairing interaction be analyzed, but also the isospin symmetry breaking cases. More importantly, the number operator of the np-pairs can be realized in this neutron and proton quasi-spin basis, with which the np-pair occupation number and its fluctuation at the J = 0

^{+}

ground state of the model can be evaluated. As examples of the application, binding energies and low-lying J =

0^{+}

excited states of the even–even and odd–odd N∼Z

d s

-shell nuclei are fit in the model with the charge-independent approximation, from which the neutron–proton pairing contribution to the binding energy in the

d s

-shell nuclei is estimated. It is observed that the decrease in the double binding-energy difference for the odd–odd nuclei is mainly due to the symmetry energy and Wigner energy contribution to the binding energy that alter the pairing staggering patten. The np-pair amplitudes in the np-pair stripping or picking-up process of these N = Z nuclei are also calculated. Full article

(This article belongs to the Special Issue Experiments and Theories of Radioactive Nuclear Beam Physics)

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