{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:05:47Z","timestamp":1760144747596,"version":"build-2065373602"},"reference-count":178,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T00:00:00Z","timestamp":1716163200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Strategic Priority Research Program of Chinese Academy of Sciences","award":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"],"award-info":[{"award-number":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"]}]},{"name":"National Natural Science Foundation of China","award":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"],"award-info":[{"award-number":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"]}]},{"name":"National Key Research and Development (R&amp;D) Program","award":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"],"award-info":[{"award-number":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"],"award-info":[{"award-number":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"]}]},{"name":"Supercomputing Center of Lanzhou University","award":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"],"award-info":[{"award-number":["XDB34000000","12275111","12075104","2021YFA1601500","lzujbky-2022-sp02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The pseudo-spin symmetry (PSS) provides an important angle to understand nuclear microscopic structure and the novel phenomena found in unstable nuclei. The relativistic Hartree\u2013Fock (RHF) theory, that takes the important degrees of freedom associated with the \u03c0-meson and \u03c1-tensor (\u03c1-T) couplings into account, provides an appropriate description of the PSS restoration in realistic nuclei, particularly for the pseudo-spin (PS) doublets with high angular momenta (l\u02dc). The investigations of the PSS within the RHF theory are recalled in this paper by focusing on the effects of the Fock terms. Aiming at common artificial shell closures appearing in previous relativistic mean-field calculations, the mechanism responsible for the PSS restoration of high-l\u02dc orbits is stressed, revealing the manifestation of nuclear in-medium effects on the PSS, and thus, providing qualitative guidance on modeling the in-medium balance between nuclear attractions and repulsions. Moreover, the essential role played by the \u03c1-T coupling, that contributes mainly via the Fock terms, is introduced as combined with the relations between the PSS and various nuclear phenomena, including the shell structure and the evolution, novel halo and bubble-like phenomena, and the superheavy magicity. As the consequences of the nuclear force in complicated nuclear many-body systems, the PSS itself and the mechanism therein can not only deepen our understanding of nuclear microscopic structure and relevant phenomena, but also provide special insight into the nature of the nuclear force, which can further enrich our knowledge of nuclear physics.<\/jats:p>","DOI":"10.3390\/sym16050631","type":"journal-article","created":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T11:06:41Z","timestamp":1716203201000},"page":"631","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Pseudo-Spin Symmetry and the Hints for Unstable and Superheavy Nuclei"],"prefix":"10.3390","volume":"16","author":[{"given":"Jing","family":"Geng","sequence":"first","affiliation":[{"name":"School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China"}]},{"given":"Zhiheng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China"},{"name":"Frontier Science Center for Rare Isotope, Lanzhou University, Lanzhou 730000, China"},{"name":"Joint Department for Nuclear Physics, Lanzhou University and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China"}]},{"given":"Jia","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8635-3939","authenticated-orcid":false,"given":"Jiajie","family":"Li","sequence":"additional","affiliation":[{"name":"School of Physical Science and Technology, Southwest University, Chongqing 400715, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3245-765X","authenticated-orcid":false,"given":"Wenhui","family":"Long","sequence":"additional","affiliation":[{"name":"School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China"},{"name":"Frontier Science Center for Rare Isotope, Lanzhou University, Lanzhou 730000, China"},{"name":"Joint Department for Nuclear Physics, Lanzhou University and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"694c","DOI":"10.1016\/j.nuclphysa.2010.01.126","article-title":"Progress in HIRFL-CSR","volume":"834","author":"Zhan","year":"2010","journal-title":"Nucl. Phys. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"717c","DOI":"10.1016\/j.nuclphysa.2010.01.130","article-title":"SPIRAL2 at GANIL: Next Generation of ISOL Facility for Intense Secondary Radioactive Ion Beams","volume":"834","author":"Gales","year":"2010","journal-title":"Nucl. Phys. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"707c","DOI":"10.1016\/j.nuclphysa.2010.01.128","article-title":"RIKEN RI Beam Factory\u2014Recent Results and Perspectives","volume":"834","author":"Motobayashi","year":"2010","journal-title":"Nucl. Phys. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"682c","DOI":"10.1016\/j.nuclphysa.2010.01.124","article-title":"1, 2, 3\u2026FAIR!","volume":"834","author":"Sturm","year":"2010","journal-title":"Nucl. Phys. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"688c","DOI":"10.1016\/j.nuclphysa.2010.01.125","article-title":"Plans for the Facility for Rare Isotope Beams","volume":"834","author":"Thoennessen","year":"2010","journal-title":"Nucl. Phys. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.nimb.2013.05.058","article-title":"Experimental systems overview of the Rare Isotope Science Project in Korea","volume":"317","author":"Tshoo","year":"2013","journal-title":"Nucl. Instr. Meth. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/0146-6410(95)00046-L","article-title":"Nuclear Structure Studies from Reaction Induced by Radioactive Nuclear Beams","volume":"35","author":"Tanihata","year":"1995","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"S171","DOI":"10.1016\/S0146-6410(00)90013-9","article-title":"The Study of Exotic Nuclei","volume":"45","author":"Casten","year":"2000","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1103\/RevModPhys.76.215","article-title":"Structure and reactions of quantum halos","volume":"76","author":"Jensen","year":"2004","journal-title":"Rev. Mod. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2003.07.004","article-title":"Light dripline nuclei","volume":"389","author":"Jonson","year":"2004","journal-title":"Phys. Rep."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/0370-2693(95)00012-A","article-title":"Large deformation of the very neutron-rich nucleus 32Mg from intermediate-energy Coulomb excitation","volume":"346","author":"Motobayashi","year":"1995","journal-title":"Phys. Lett. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1103\/PhysRevLett.83.496","article-title":"Direct Experimental Evidence for Strong Admixture of Different Parity States in 11Li","volume":"83","author":"Simon","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5493","DOI":"10.1103\/PhysRevLett.84.5493","article-title":"New Magic Number, N = 16, near the Neutron Drip Line","volume":"84","author":"Ozawa","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"152502","DOI":"10.1103\/PhysRevLett.100.152502","article-title":"Determination of the N = 16 Shell Closure at the Oxygen Drip Line","volume":"100","author":"Hoffman","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"152501","DOI":"10.1103\/PhysRevLett.102.152501","article-title":"One-Neutron Removal Measurement Reveals 24O as a New Doubly Magic Nucleus","volume":"102","author":"Kanungo","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"022501","DOI":"10.1103\/PhysRevLett.109.022501","article-title":"N = 16 Spherical Shell Closure in 24O","volume":"109","author":"Tshoo","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1038\/nature12522","article-title":"Evidence for a new nuclear \u2019magic number\u2019 from the level structure of 54Ca","volume":"502","author":"Steppenbeck","year":"2013","journal-title":"Nature"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"252501","DOI":"10.1103\/PhysRevLett.114.252501","article-title":"Low-Lying Structure of 50Ar and the N = 32 Subshell Closure","volume":"114","author":"Steppenbeck","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1088\/0031-8949\/28\/3\/010","article-title":"Discussions with Jens Lindhard","volume":"28","author":"Swiatecki","year":"1983","journal-title":"Phys. Scr."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0370-2693(74)90593-0","article-title":"Bubbles and the odd-state force","volume":"48","author":"Saunier","year":"1974","journal-title":"Phys. Lett. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0370-2693(73)90121-4","article-title":"Possible bubble nuclei -36Ar and 200Hg","volume":"46","author":"Campi","year":"1973","journal-title":"Phys. Lett. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.nuclphysa.2007.11.012","article-title":"Detecting bubbles in exotic nuclei","volume":"800","author":"Khan","year":"2008","journal-title":"Nucl. Phys. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"034318","DOI":"10.1103\/PhysRevC.79.034318","article-title":"Nuclear \u2019bubble\u2019 structure in 34Si","volume":"79","author":"Grasso","year":"2009","journal-title":"Phys. Rev. C"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"067305","DOI":"10.1103\/PhysRevC.87.067305","article-title":"Tensor-force effects on single-particle levels and proton bubble structure around the Z or N = 20 magic number","volume":"87","author":"Nakada","year":"2013","journal-title":"Phys. Rev. C"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"021301","DOI":"10.1103\/PhysRevC.69.021301","article-title":"Spin-orbit splitting in low-j neutron orbits and proton densities in the nuclear interior","volume":"69","author":"Piekarewicz","year":"2004","journal-title":"Phys. Rev. C"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"044333","DOI":"10.1103\/PhysRevC.84.044333","article-title":"Tensor effects on the proton sd states in neutron-rich Ca isotopes and bubble structure of exotic nuclei","volume":"84","author":"Wang","year":"2011","journal-title":"Phys. Rev. C"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"017302","DOI":"10.1103\/PhysRevC.91.017302","article-title":"Effect of a tensor force on the proton bubble structure of 206Hg","volume":"91","author":"Wang","year":"2015","journal-title":"Phys. Rev. C"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"024308","DOI":"10.1103\/PhysRevC.71.024308","article-title":"Central depression in nuclear density and its consequences for the shell structure of superheavy nuclei","volume":"71","author":"Afanasjev","year":"2005","journal-title":"Phys. Rev. C"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"034302","DOI":"10.1103\/PhysRevC.71.034302","article-title":"Density distributions of superheavy nuclei","volume":"71","author":"Pei","year":"2005","journal-title":"Phys. Rev. C"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/S0370-2693(99)00225-7","article-title":"Superheavy and hyperheavy nuclei in the form of bubbles or semi-bubbles","volume":"451","author":"Berger","year":"1999","journal-title":"Phys. Lett. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"054312","DOI":"10.1103\/PhysRevC.93.054312","article-title":"Pseudospin-orbit splitting and its consequences for the central depression in nuclear density","volume":"93","author":"Li","year":"2016","journal-title":"Phys. Rev. C"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.physletb.2018.11.034","article-title":"48Si: An atypical nucleus?","volume":"788","author":"Li","year":"2019","journal-title":"Phys. Lett. B"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.ppnp.2019.02.008","article-title":"Current status of r-process nucleosynthesis","volume":"107","author":"Kajino","year":"2019","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"015002","DOI":"10.1103\/RevModPhys.93.015002","article-title":"Origin of the heaviest elements: The rapid neutron-capture process","volume":"93","author":"Cowan","year":"2021","journal-title":"Rev. Mod. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"044602","DOI":"10.1103\/PhysRevC.74.044602","article-title":"Synthesis of the isotopes of elements 118 and 116 in the 249Cf and 245Cm + 48Ca fusion reactions","volume":"74","author":"Oganessian","year":"2006","journal-title":"Phys. Rev. C"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"142502","DOI":"10.1103\/PhysRevLett.104.142502","article-title":"Synthesis of a New Element with Atomic Number Z = 117","volume":"104","author":"Oganessian","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"054608","DOI":"10.1103\/PhysRevC.79.054608","article-title":"Stability of superheavy nuclei produced in actinide-based complete fusion reactions: Evidence for the next magic proton number at Z \u2a7e 120","volume":"79","author":"Adamian","year":"2009","journal-title":"Phys. Rev. C"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/0370-2693(69)90443-2","article-title":"Pseudo LS coupling and pseudo SU(3) coupling schemes","volume":"30","author":"Arima","year":"1969","journal-title":"Phys. Lett. B"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/0375-9474(69)90077-3","article-title":"Generalized seniority for favored J \u2260 0 pairs in mixed configurations","volume":"137","author":"Hecht","year":"1969","journal-title":"Nucl. Phys. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0370-1573(99)00021-6","article-title":"A relativistic symmetry in nuclei","volume":"315","author":"Ginocchio","year":"1999","journal-title":"Phys. Rep."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.physrep.2005.04.003","article-title":"Relativistic symmetries in nuclei and hadrons","volume":"414","author":"Ginocchio","year":"2005","journal-title":"Phys. Rep."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2014.12.005","article-title":"Hidden pseudospin and spin symmetries and their origins in atomic nuclei","volume":"570","author":"Liang","year":"2015","journal-title":"Phys. Rep."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"103713","DOI":"10.1016\/j.ppnp.2019.103713","article-title":"Towards an ab initio covariant density functional theory for nuclear structure","volume":"109","author":"Shen","year":"2019","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1103\/PhysRevLett.78.436","article-title":"Pseudospin as a Relativistic Symmetry","volume":"78","author":"Ginocchio","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1103\/PhysRevC.5.241","article-title":"Relativistic self-consistent meson field theory of spherical nuclei","volume":"5","author":"Miller","year":"1972","journal-title":"Phys. Rev. C"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"R628","DOI":"10.1103\/PhysRevC.58.R628","article-title":"Pseudospin symmetry in relativistic mean field theory","volume":"58","author":"Meng","year":"1998","journal-title":"Phys. Rev. C"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1103\/PhysRevLett.47.1259","article-title":"Proton Single-Particle States above Z = 64","volume":"47","author":"Nagai","year":"1981","journal-title":"Phys. Rev. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"034314","DOI":"10.1103\/PhysRevC.76.034314","article-title":"Shell structure and \u03c1-tensor correlations in density dependent relativistic Hartree-Fock theory","volume":"76","author":"Long","year":"2007","journal-title":"Phys. Rev. C"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.physletb.2009.09.034","article-title":"Non-local mean field effect on nuclei near sub-shell","volume":"680","author":"Long","year":"2009","journal-title":"Phys. Lett. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"024308","DOI":"10.1103\/PhysRevC.81.024308","article-title":"Relativistic Hartree-Fock-Bogoliubov theory with density dependent meson-nucleon couplings","volume":"81","author":"Long","year":"2010","journal-title":"Phys. Rev. C"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.physletb.2014.03.031","article-title":"Superheavy magic structures in the relativistic Hartree-Fock-Bogoliubov approach","volume":"732","author":"Li","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1134\/S106377880705002X","article-title":"Pseudospin symmetry and structure of nuclei with Z \u2265 100","volume":"70","author":"Jolos","year":"2007","journal-title":"Phys. Atom. Nucl."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1103\/PhysRevLett.59.1405","article-title":"Abundance and systematics of nuclear superdeformed states; relation to the pseudospin and pseudo-SU(3) symmetries","volume":"59","author":"Dudek","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1103\/PhysRevLett.68.2133","article-title":"Pseudospin symmetry in nuclear physics","volume":"68","author":"Bahri","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/0003-4916(74)90208-5","article-title":"A theory of highly condensed matter","volume":"83","author":"Walecka","year":"1974","journal-title":"Ann. Phys."},{"key":"ref_56","first-page":"48","article-title":"On the interaction of elementary particles","volume":"17","author":"Yukawa","year":"1935","journal-title":"Proc. Phys. Math. Soc. Jpn."},{"key":"ref_57","first-page":"1","article-title":"The relativistic nuclear many-body problem","volume":"16","author":"Serot","year":"1986","journal-title":"Adv. Nucl. Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0375-9474(98)00178-X","article-title":"Relativistic continuum Hartree-Bogoliubov theory with both zero range and finite range Gogny force and their application","volume":"635","author":"Meng","year":"1998","journal-title":"Nucl. Phys. A"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.physrep.2004.10.001","article-title":"Relativistic Hartree-Bogoliubov theory: Static and dynamic aspects of exotic nuclear structure","volume":"409","author":"Vretenar","year":"2005","journal-title":"Phys. Rep."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1063\/1.2398833","article-title":"Toward a deformed relativistic Hartree Bogoliubov model for exotic nuclei","volume":"865","author":"Zhou","year":"2006","journal-title":"AIP Conf. Proc."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.ppnp.2005.06.001","article-title":"Relativistic continuum Hartree Bogoliubov theory for ground-state properties of exotic nuclei","volume":"57","author":"Meng","year":"2006","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"024312","DOI":"10.1103\/PhysRevC.85.024312","article-title":"Deformed relativistic Hartree-Bogoliubov theory in continuum","volume":"85","author":"Li","year":"2012","journal-title":"Phys. Rev. C"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"067301","DOI":"10.1103\/PhysRevC.85.067301","article-title":"Density-dependent deformed relativistic Hartree-Bogoliubov theory in continuum","volume":"85","author":"Chen","year":"2012","journal-title":"Phys. Rev. C"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"3963","DOI":"10.1103\/PhysRevLett.77.3963","article-title":"Relativistic Hartree-Bogoliubov Description of the Neutron Halo in 11Li","volume":"77","author":"Meng","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1103\/PhysRevLett.80.460","article-title":"Giant halo at the neutron drip line","volume":"80","author":"Meng","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0370-2693(97)01386-5","article-title":"The proton and neutron distributions in Na isotopes: The development of halo and shell","volume":"419","author":"Meng","year":"1998","journal-title":"Phys. Lett. B"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"011301","DOI":"10.1103\/PhysRevC.82.011301","article-title":"Neutron halo in deformed nuclei","volume":"82","author":"Zhou","year":"2010","journal-title":"Phys. Rev. C"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"054315","DOI":"10.1103\/PhysRevC.103.054315","article-title":"Deformed two-neutron halo in 19B","volume":"103","author":"Sun","year":"2021","journal-title":"Phys. Rev. C"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"014334","DOI":"10.1103\/PhysRevC.87.014334","article-title":"Pseudospin symmetry in supersymmetric quantum mechanics: Schr\u00f6dinger equations","volume":"87","author":"Liang","year":"2013","journal-title":"Phys. Rev. C"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"024311","DOI":"10.1103\/PhysRevC.88.024311","article-title":"Pseudospin symmetry in supersymmetric quantum mechanics. II. Spin-orbit effects","volume":"88","author":"Shen","year":"2013","journal-title":"Phys. Rev. C"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"5015","DOI":"10.1103\/PhysRevLett.86.5015","article-title":"Isospin Asymmetry in the Pseudospin Dynamical Symmetry","volume":"86","author":"Alberto","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"034307","DOI":"10.1103\/PhysRevC.65.034307","article-title":"Pseudospin symmetry as a relativistic dynamical symmetry in the nucleus","volume":"65","author":"Alberto","year":"2002","journal-title":"Phys. Rev. C"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"054313","DOI":"10.1103\/PhysRevC.105.054313","article-title":"Investigation of pseudospin and spin symmetries in relativistic mean field theory combined with a similarity renormalization group approach","volume":"105","author":"Huang","year":"2022","journal-title":"Phys. Rev. C"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/S0370-2693(01)00737-7","article-title":"On the sufficient conditions for the pseudospin symmetry in relativistic models","volume":"513","author":"Marcos","year":"2001","journal-title":"Phys. Lett. B"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"064324","DOI":"10.1103\/PhysRevC.81.064324","article-title":"Spin and pseudospin symmetries in the antinucleon spectrum of nuclei","volume":"81","author":"Lisboa","year":"2010","journal-title":"Phys. Rev. C"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"012037","DOI":"10.1088\/1742-6596\/267\/1\/012037","article-title":"Relativistic U(3) symmetry and pseudo-U(3) symmetry of the Dirac Hamiltonian","volume":"267","author":"Ginocchio","year":"2011","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"R45","DOI":"10.1103\/PhysRevC.58.R45","article-title":"Relativistic mean field approach and the pseudospin symmetry","volume":"58","author":"Lalazissis","year":"1998","journal-title":"Phys. Rev. C"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"R3065","DOI":"10.1103\/PhysRevC.58.R3065","article-title":"Hidden pseudospin symmetry in the Dirac equation","volume":"58","author":"Arima","year":"1998","journal-title":"Phys. Rev. C"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"064312","DOI":"10.1103\/PhysRevC.66.064312","article-title":"Pseudospin symmetry and relativistic mean field eigenfunctions","volume":"66","author":"Ginocchio","year":"2002","journal-title":"Phys. Rev. C"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"054313","DOI":"10.1103\/PhysRevC.65.054313","article-title":"Spin symmetry and pseudospin symmetry in the relativistic mean field with a deformed potential","volume":"65","author":"Yamaji","year":"2002","journal-title":"Phys. Rev. C"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"034303","DOI":"10.1103\/PhysRevC.69.034303","article-title":"Test of pseudospin symmetry in deformed nuclei","volume":"69","author":"Ginocchio","year":"2004","journal-title":"Phys. Rev. C"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"014323","DOI":"10.1103\/PhysRevC.109.014323","article-title":"Probing spin and pseudospin symmetries in deformed nuclei by the Green\u2019s function method","volume":"109","author":"Sun","year":"2024","journal-title":"Phys. Rev. C"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"137716","DOI":"10.1016\/j.physletb.2023.137716","article-title":"Pseudospin symmetry in resonant states in deformed nuclei","volume":"838","author":"Zhang","year":"2023","journal-title":"Phys. Lett. B"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"044312","DOI":"10.1103\/PhysRevC.96.044312","article-title":"Spin and pseudospin symmetries in the single-\u039b spectrum","volume":"96","author":"Sun","year":"2017","journal-title":"Phys. Rev. C"},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"125104","DOI":"10.1088\/1361-6471\/aa8e2d","article-title":"(Pseudo)spin symmetry in the single-neutron spectrum of \u039b hypernuclei","volume":"44","author":"Lu","year":"2017","journal-title":"J. Phys. G Nucl. Part. Phys."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"054319","DOI":"10.1103\/PhysRevC.72.054319","article-title":"Pseudospin symmetry in the resonant states of nuclei","volume":"72","author":"Guo","year":"2005","journal-title":"Phys. Rev. C"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"024320","DOI":"10.1103\/PhysRevC.74.024320","article-title":"Isospin dependence of pseudospin symmetry in nuclear resonant states","volume":"74","author":"Guo","year":"2006","journal-title":"Phys. Rev. C"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"052122","DOI":"10.1103\/PhysRevA.87.052122","article-title":"Resonant states and pseudospin symmetry in the Dirac-Morse potential","volume":"87","author":"Liu","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"072501","DOI":"10.1103\/PhysRevLett.109.072501","article-title":"Pseudospin Symmetry in Single Particle Resonant States","volume":"109","author":"Lu","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"024323","DOI":"10.1103\/PhysRevC.88.024323","article-title":"Pseudospin symmetry in single-particle resonances in spherical square wells","volume":"88","author":"Lu","year":"2013","journal-title":"Phys. Rev. C"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"124102","DOI":"10.1088\/1674-1137\/ac23d4","article-title":"Influence of different fields of mesons on the pseudospin symmetry in single-neutron resonant states","volume":"45","author":"Dai","year":"2021","journal-title":"Chin. Phys. C"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"034310","DOI":"10.1103\/PhysRevC.99.034310","article-title":"Green\u2019s function method for the spin and pseudospin symmetries in the single-particle resonant states","volume":"99","author":"Sun","year":"2019","journal-title":"Phys. Rev. C"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1140\/epja\/i2019-12725-3","article-title":"Isospin asymmetry of the pseudospin symmetry in nuclear resonant states","volume":"55","author":"Xu","year":"2019","journal-title":"Eur. Phys. J. A"},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"138320","DOI":"10.1016\/j.physletb.2023.138320","article-title":"Conservation and breaking of pseudospin symmetry","volume":"847","author":"Sun","year":"2023","journal-title":"Phys. Lett. B"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"136829","DOI":"10.1016\/j.physletb.2021.136829","article-title":"Pseudospin symmetry in resonant states and its dependence on the shape of potential","volume":"824","author":"Liu","year":"2022","journal-title":"Phys. Lett. B"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"135174","DOI":"10.1016\/j.physletb.2019.135174","article-title":"Pseudospin and spin symmetries in single particle resonant states in Pb isotopes","volume":"801","author":"Shi","year":"2020","journal-title":"Phys. Lett. B"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"1281","DOI":"10.1103\/PhysRevLett.28.1281","article-title":"Possible Validity of the Relativistic Hartree-Fock Approximation in Nuclear Physics","volume":"28","author":"Miller","year":"1972","journal-title":"Phys. Rev. Lett."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"1510","DOI":"10.1103\/PhysRevC.18.1510","article-title":"Relativistic Hartree-Fock description of nuclei","volume":"18","author":"Brockmann","year":"1978","journal-title":"Phys. Rev. C"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1103\/PhysRevC.36.380","article-title":"Relativistic description of nuclear systems in the Hartree-Fock approximation","volume":"36","author":"Bouyssy","year":"1987","journal-title":"Phys. Rev. C"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.physletb.2006.05.065","article-title":"Pseudo-spin symmetry in density-dependent relativistic Hartree-Fock theory","volume":"639","author":"Long","year":"2006","journal-title":"Phys. Lett. B"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"12001","DOI":"10.1209\/0295-5075\/82\/12001","article-title":"Evolution of nuclear shell structure due to the pion exchange potential","volume":"82","author":"Long","year":"2008","journal-title":"Europhys. Lett."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"047301","DOI":"10.1103\/PhysRevC.87.047301","article-title":"Tensor effects on the evolution of the N = 40 shell gap from nonrelativistic and relativistic mean-field theory","volume":"87","author":"Wang","year":"2013","journal-title":"Phys. Rev. C"},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1140\/epja\/i2010-10938-6","article-title":"Spin symmetry in Dirac negative-energy spectrum in density-dependent relativistic Hartree-Fock theory","volume":"44","author":"Liang","year":"2010","journal-title":"Eur. Phys. J. A"},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"051301","DOI":"10.1103\/PhysRevC.100.051301","article-title":"Pseudospin symmetry restoration and the in-medium balance between nuclear attractive and repulsive interactions","volume":"100","author":"Geng","year":"2019","journal-title":"Phys. Rev. C"},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"065805","DOI":"10.1103\/PhysRevC.78.065805","article-title":"Neutron star properties in density-dependent relativistic Hartree-Fock theory","volume":"78","author":"Sun","year":"2008","journal-title":"Phys. Rev. C"},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"025802","DOI":"10.1103\/PhysRevC.91.025802","article-title":"Self-consistent tensor effects on nuclear matter systems within a relativistic Hartree-Fock approach","volume":"91","author":"Jiang","year":"2015","journal-title":"Phys. Rev. C"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"034326","DOI":"10.1103\/PhysRevC.91.034326","article-title":"Nuclear tensor interaction in a covariant energy density functional","volume":"91","author":"Jiang","year":"2015","journal-title":"Phys. Rev. C"},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"034313","DOI":"10.1103\/PhysRevC.98.034313","article-title":"Quantitative analysis of tensor effects in the relativistic Hartree-Fock theory","volume":"98","author":"Wang","year":"2018","journal-title":"Phys. Rev. C"},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"031302","DOI":"10.1103\/PhysRevC.81.031302","article-title":"Nuclear halo structure and pseudospin symmetry","volume":"81","author":"Long","year":"2010","journal-title":"Phys. Rev. C"},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.physletb.2015.12.004","article-title":"Magicity of neutron-rich nuclei within relativistic self-consistent approaches","volume":"753","author":"Li","year":"2016","journal-title":"Phys. Lett. B"},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"135524","DOI":"10.1016\/j.physletb.2020.135524","article-title":"New magicity N = 32 and 34 due to strong couplings between Dirac inversion partners","volume":"806","author":"Liu","year":"2020","journal-title":"Phys. Lett. B"},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1088\/0034-4885\/52\/4\/002","article-title":"The relativistic mean-field description of nuclei and nuclear dynamics","volume":"52","author":"Reinhard","year":"1989","journal-title":"Rep. Prog. Phys."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/0375-9474(77)90626-1","article-title":"Relativistic calculation of nuclear matter and the nuclear surface","volume":"292","author":"Boguta","year":"1977","journal-title":"Nucl. Phys. A"},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/0375-9474(94)90923-7","article-title":"Relativistic mean-field theory for unstable nuclei with non-linear \u03c3 and \u03c9 terms","volume":"579","author":"Sugahara","year":"1994","journal-title":"Nucl. Phys. A"},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"034319","DOI":"10.1103\/PhysRevC.69.034319","article-title":"New effective interactions in relativistic mean field theory with nonlinear terms and density-dependent meson-nucleon coupling","volume":"69","author":"Long","year":"2004","journal-title":"Phys. Rev. C"},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"3408","DOI":"10.1103\/PhysRevLett.68.3408","article-title":"Relativistic density-dependent Hartree approcah for finite nuclei","volume":"68","author":"Brockmann","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/0370-2693(94)01664-X","article-title":"Rearrangement in the density dependent relativistic field theory of nuclei","volume":"345","author":"Lenske","year":"1995","journal-title":"Phys. Lett. B"},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"3043","DOI":"10.1103\/PhysRevC.52.3043","article-title":"Density dependent hadron field theory","volume":"52","author":"Fuchs","year":"1995","journal-title":"Phys. Rev. C"},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/S0375-9474(99)00310-3","article-title":"Relativistic mean field calculations with density-dependent meson-nucleon coupling","volume":"656","author":"Typel","year":"1999","journal-title":"Nucl. Phys. A"},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"2665","DOI":"10.1103\/PhysRevC.48.2665","article-title":"Relativistic Hartree-Fock approximation in a nonlinear model for nuclear matter and finite nuclei","volume":"48","author":"Bernardos","year":"1993","journal-title":"Phys. Rev. C"},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1088\/0954-3899\/30\/6\/002","article-title":"Description of nuclear systems within the relativistic Hartree-Fock method with zero-range self-interactions of the scalar field","volume":"30","author":"Marcos","year":"2004","journal-title":"J. Phys. G Nucl. Part. Phys."},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.physletb.2006.07.064","article-title":"Density-dependent relativistic Hartree-Fock approach","volume":"640","author":"Long","year":"2006","journal-title":"Phys. Lett. B"},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"054309","DOI":"10.1103\/PhysRevC.84.054309","article-title":"Relativistic mean-field interaction with density-dependent meson-nucleon vertices based on microscopical calculations","volume":"84","author":"Centelles","year":"2011","journal-title":"Phys. Rev. C"},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"054317","DOI":"10.1103\/PhysRevC.86.054317","article-title":"Dirac-Brueckner-Hartree-Fock versus chiral effective field theory","volume":"86","author":"Sammarruca","year":"2012","journal-title":"Phys. Rev. C"},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/S0375-9474(02)00750-9","article-title":"Interplay of three-body interactions in the EOS of nuclear matter","volume":"706","author":"Zuo","year":"2002","journal-title":"Nucl. Phys. A"},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.physletb.2018.03.080","article-title":"Spin symmetry in the Dirac sea derived from the bare nucleon-nucleon interaction","volume":"781","author":"Shen","year":"2018","journal-title":"Phys. Lett. B"},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.physletb.2018.01.058","article-title":"Effects of tensor forces in nuclear spin-orbit splittings from ab initio calculations","volume":"778","author":"Shen","year":"2018","journal-title":"Phys. Lett. B"},{"key":"ref_128","doi-asserted-by":"crossref","first-page":"054312","DOI":"10.1103\/PhysRevC.97.054312","article-title":"Relativistic Brueckner-Hartree-Fock theory for neutron drops","volume":"97","author":"Shen","year":"2018","journal-title":"Phys. Rev. C"},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"142002","DOI":"10.1103\/PhysRevLett.128.142002","article-title":"Accurate Relativistic Chiral Nucleon-Nucleon Interaction up to Next-to-Next-to-Leading Order","volume":"128","author":"Lu","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_130","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1088\/0256-307X\/23\/5\/021","article-title":"Spurious Shell Closures in the relativistic mean field model","volume":"23","author":"Geng","year":"2006","journal-title":"Chin. Phys. Lett."},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0370-1573(74)90008-8","article-title":"Current status of the relativistic two-nucleon one boson exhcange potential","volume":"13","author":"Erkelenz","year":"1974","journal-title":"Phys. Rep."},{"doi-asserted-by":"crossref","unstructured":"Meng, J. (2016). Relativistic Density Functional for Nuclear Structure, World Scientific Publishing. International Review of Nuclear Physics Volume 10.","key":"ref_132","DOI":"10.1142\/9872"},{"key":"ref_133","doi-asserted-by":"crossref","first-page":"064302","DOI":"10.1103\/PhysRevC.101.064302","article-title":"Relativistic Hartree-Fock model for axially deformed nuclei","volume":"101","author":"Geng","year":"2020","journal-title":"Phys. Rev. C"},{"key":"ref_134","doi-asserted-by":"crossref","first-page":"097301","DOI":"10.1088\/1572-9494\/ac70ae","article-title":"Relativistic Hartree-Fock model and its recent progress on the description of nuclear structure","volume":"74","author":"Long","year":"2022","journal-title":"Commun. Theor. Phys."},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1103\/PhysRev.108.1175","article-title":"Theory of Superconductivity","volume":"108","author":"Bardeen","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_136","first-page":"244","article-title":"A variation principle in the problem of many bodies","volume":"119","author":"Bogoliubov","year":"1958","journal-title":"Dokl. Akad. Nauk. SSSR"},{"key":"ref_137","first-page":"1011","article-title":"On a Variational Principle in the Many Body Problem","volume":"124","author":"Bogoliubov","year":"1959","journal-title":"Dokl. Akad. Nauk. SSSR"},{"key":"ref_138","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1103\/PhysRev.122.1012","article-title":"Generalized Hartree-Fock Method","volume":"122","author":"Valatin","year":"1961","journal-title":"Phys. Rev."},{"doi-asserted-by":"crossref","unstructured":"Ring, P., and Schuck, P. (1980). The Nuclear Many-Body Problem, Springer.","key":"ref_139","DOI":"10.1007\/978-3-642-61852-9"},{"key":"ref_140","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.physletb.2009.04.067","article-title":"A finite range pairing force for density functional theory in superfluid nuclei","volume":"676","author":"Tian","year":"2009","journal-title":"Phys. Lett. B"},{"key":"ref_141","doi-asserted-by":"crossref","first-page":"034329","DOI":"10.1103\/PhysRevC.105.034329","article-title":"Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei","volume":"105","author":"Geng","year":"2022","journal-title":"Phys. Rev. C"},{"key":"ref_142","doi-asserted-by":"crossref","first-page":"024312","DOI":"10.1103\/PhysRevC.71.024312","article-title":"New relativistic mean-field interaction with density-dependent meson-nucleon couplings","volume":"71","author":"Lalazissis","year":"2005","journal-title":"Phys. Rev. C"},{"key":"ref_143","doi-asserted-by":"crossref","first-page":"074107","DOI":"10.1088\/1674-1137\/44\/7\/074107","article-title":"Novel relativistic mean field Lagrangian guided by pseudo-spin symmetry restoration","volume":"44","author":"Wei","year":"2020","journal-title":"Chin. Rhys. C"},{"key":"ref_144","doi-asserted-by":"crossref","first-page":"B864","DOI":"10.1103\/PhysRev.136.B864","article-title":"Inhomogeneous Electron Gas","volume":"136","author":"Hohenberg","year":"1964","journal-title":"Phys. Rev."},{"key":"ref_145","doi-asserted-by":"crossref","first-page":"A1133","DOI":"10.1103\/PhysRev.140.A1133","article-title":"Self-Consistent Equations Including Exchange and Correlation Effects","volume":"140","author":"Kohn","year":"1965","journal-title":"Phys. Rev."},{"key":"ref_146","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.physletb.2017.03.074","article-title":"New short-lived isotope 223Np and the absence of the Z = 92 subshell closure near N = 126","volume":"771","author":"Sun","year":"2017","journal-title":"Phys. Lett. B"},{"key":"ref_147","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1088\/0034-4885\/70\/9\/R02","article-title":"Nuclear structure and astrophysics","volume":"70","author":"Grawe","year":"2007","journal-title":"Rep. Prog. Phys."},{"key":"ref_148","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/0375-9474(84)90240-9","article-title":"Microscopic analysis of collective dynamics in low energy fission","volume":"428","author":"Berger","year":"1984","journal-title":"Nucl. Phys. A"},{"key":"ref_149","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0375-9474(98)00180-8","article-title":"A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities","volume":"635","author":"Chabanat","year":"1998","journal-title":"Nucl. Phys. A"},{"key":"ref_150","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.physletb.2008.11.070","article-title":"The effective force NL3 revisited","volume":"671","author":"Lalazissis","year":"2009","journal-title":"Phys. Lett. B"},{"key":"ref_151","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.physrep.2003.09.006","article-title":"Nuclear spinodal fragmentation","volume":"389","author":"Chomaz","year":"2004","journal-title":"Phys. Rep."},{"key":"ref_152","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2004.10.002","article-title":"The thermodynamic model for nuclear multifragmentation","volume":"406","author":"Das","year":"2005","journal-title":"Phys. Rep."},{"key":"ref_153","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.physrep.2006.12.002","article-title":"Vector manifestation and matter formed in relativistic heavy-ion processes","volume":"439","author":"Brown","year":"2007","journal-title":"Phys. Rep."},{"key":"ref_154","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.physrep.2008.04.005","article-title":"Recent progress and new challenges in isospin physics with heavy-ion reactions","volume":"464","author":"Li","year":"2008","journal-title":"Phys. Rep."},{"key":"ref_155","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1103\/RevModPhys.64.1133","article-title":"Cooling of neutron stars","volume":"64","author":"Pethick","year":"1992","journal-title":"Rev. Mod. Phys."},{"key":"ref_156","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0370-1573(96)00023-3","article-title":"Composition and structure of protoneutron stars","volume":"280","author":"Prakash","year":"1997","journal-title":"Phys. Rep."},{"key":"ref_157","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1126\/science.1090720","article-title":"The Physics of Neutron Stars","volume":"304","author":"Lattimer","year":"2004","journal-title":"Science"},{"key":"ref_158","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.physrep.2015.12.005","article-title":"The equation of state of hot, dense matter and neutron stars","volume":"621","author":"Lattimer","year":"2016","journal-title":"Phys. Rep."},{"key":"ref_159","doi-asserted-by":"crossref","first-page":"4980","DOI":"10.1093\/mnras\/stz293","article-title":"Neutron star collapse and gravitational waves with a non-convex equation of state","volume":"484","author":"Aloy","year":"2019","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_160","doi-asserted-by":"crossref","first-page":"2072","DOI":"10.1103\/PhysRevC.52.2072","article-title":"Phase transitions in warm, asymmetric nuclear matter","volume":"52","author":"Serot","year":"1995","journal-title":"Phys. Rev. C"},{"key":"ref_161","doi-asserted-by":"crossref","first-page":"064304","DOI":"10.1103\/PhysRevC.81.064304","article-title":"Nuclear symmetry energy effects on liquid-gas phase transition in hot asymmetric nuclear matter","volume":"81","author":"Sharma","year":"2010","journal-title":"Phys. Rev. C"},{"key":"ref_162","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.physletb.2013.01.066","article-title":"Liquid-gas phase transition in hot asymmetric nuclear matter with density-dependent relativistic mean-field models","volume":"720","author":"Zhang","year":"2013","journal-title":"Phys. Lett. B"},{"key":"ref_163","doi-asserted-by":"crossref","first-page":"034307","DOI":"10.1103\/PhysRevC.91.034307","article-title":"Thermal properties of asymmetric nuclear matter","volume":"91","author":"Fedoseew","year":"2015","journal-title":"Phys. Rev. C"},{"key":"ref_164","doi-asserted-by":"crossref","first-page":"065212","DOI":"10.1103\/PhysRevC.95.065212","article-title":"Critical parameters of consistent relativistic mean-field models","volume":"95","author":"Dutra","year":"2017","journal-title":"Phys. Rev. C"},{"key":"ref_165","doi-asserted-by":"crossref","first-page":"054314","DOI":"10.1103\/PhysRevC.100.054314","article-title":"Critical parameters of the liquid-gas phase transition in thermal symmetric and asymmetric nuclear matter","volume":"100","author":"Yang","year":"2019","journal-title":"Phys. Rev. C"},{"key":"ref_166","doi-asserted-by":"crossref","first-page":"014304","DOI":"10.1103\/PhysRevC.103.014304","article-title":"Liquid-gas phase transition of thermal nuclear matter and the in-medium balance between nuclear attraction and repulsion","volume":"103","author":"Yang","year":"2021","journal-title":"Phys. Rev. C"},{"key":"ref_167","doi-asserted-by":"crossref","first-page":"034315","DOI":"10.1103\/PhysRevC.106.034315","article-title":"Covariant density functional theory with localized exchange terms","volume":"106","author":"Zhao","year":"2022","journal-title":"Phys. Rev. C"},{"key":"ref_168","doi-asserted-by":"crossref","first-page":"030003","DOI":"10.1088\/1674-1137\/41\/3\/030003","article-title":"The AME2016 atomic mass evaluation (II). Tables, graphs and references","volume":"41","author":"Wang","year":"2017","journal-title":"Chin. Phys. C"},{"key":"ref_169","doi-asserted-by":"crossref","first-page":"054319","DOI":"10.1103\/PhysRevC.82.054319","article-title":"New parametrization for the nuclear covariant energy density functional with a point-coupling interaction","volume":"82","author":"Zhao","year":"2010","journal-title":"Phys. Rev. C"},{"key":"ref_170","doi-asserted-by":"crossref","first-page":"034318","DOI":"10.1103\/PhysRevC.78.034318","article-title":"Relativistic nuclear energy density functionals: Adjusting parameters to binding energies","volume":"78","author":"Vretenar","year":"2008","journal-title":"Phys. Rev. C"},{"key":"ref_171","doi-asserted-by":"crossref","first-page":"041302","DOI":"10.1103\/PhysRevC.65.041302","article-title":"Giant halo at the neutron drip line in Ca isotopes in relativistic continuum Hartree-Bogoliubov theory","volume":"65","author":"Meng","year":"2002","journal-title":"Phys. Rev. C"},{"key":"ref_172","doi-asserted-by":"crossref","first-page":"192502","DOI":"10.1103\/PhysRevLett.121.192502","article-title":"Pseudospin Symmetry and Microscopic Origin of Shape Coexistence in the 78Ni Region: A Hint from Lifetime Measurements","volume":"121","author":"Delafosse","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_173","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1103\/PhysRev.69.538","article-title":"A Spherical Shell Nuclear Model","volume":"69","author":"Wilson","year":"1946","journal-title":"Phys. Rev."},{"unstructured":"Schwierz, N., Wiedenhover, I., and Volya, A. (2007). Parameterization of the Woods-Saxon Potential for Shell-Model Calculations. arXiv.","key":"ref_174"},{"key":"ref_175","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1140\/epja\/iepja1393","article-title":"On the difference between proton and neutron spin-orbit splittings in nuclei","volume":"14","author":"Isakov","year":"2002","journal-title":"Eur. Phys. J. A"},{"unstructured":"Oros, A.-M. (1996). Study of the Coupling between Collective and Single-Particle Excitation Modes in Medium Heavy Spherical Nuclei. [Ph.D. Thesis, University of K\u00f6ln].","key":"ref_176"},{"key":"ref_177","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1038\/nphys3916","article-title":"A proton density bubble in the doubly magic 34Si nucleus","volume":"13","author":"Mutschler","year":"2017","journal-title":"Nat. Phys."},{"key":"ref_178","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0375-9474(02)01398-2","article-title":"Bubbles and semi-bubbles as a new kind of superheavy nuclei","volume":"716","author":"Berger","year":"2003","journal-title":"Nucl. Phys. A"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/5\/631\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:45:13Z","timestamp":1760107513000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/5\/631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,20]]},"references-count":178,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["sym16050631"],"URL":"https:\/\/doi.org\/10.3390\/sym16050631","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,5,20]]}}}