{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:43:58Z","timestamp":1760233438016,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,16]],"date-time":"2021-01-16T00:00:00Z","timestamp":1610755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020","award":["654002"],"award-info":[{"award-number":["654002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Isospin symmetry breaking effects on the mass-radius relation of a cold, non-accreting neutron star are studied on the basis of two Skyrme Energy Density Functionals (EDFs). One functional contains isospin symmetry breaking terms other than those typically included in Skyrme EDFs while its counterpart is of standard form. Both functionals are based on the same fitting protocol except for the observables and pseudo-observables sensitive to the isospin symmetry breaking channel. The quality of those functionals is similar in the description of terrestrial observables but choosing either of them has a non-negligible effect on the mass-radius relation and tidal deformability of a neutron star. Further investigations are needed to clarify the effects of isospin symmetry breaking on these and other observables of neutron stars that are, and will become, available.<\/jats:p>","DOI":"10.3390\/sym13010144","type":"journal-article","created":{"date-parts":[[2021,1,21]],"date-time":"2021-01-21T02:36:05Z","timestamp":1611196565000},"page":"144","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Isospin Symmetry Breaking Effects on the Mass-Radius Relation of a Neutron Star"],"prefix":"10.3390","volume":"13","author":[{"given":"Giovanni","family":"Selva","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica \u201cAldo Pontremoli\u201d, Universit\u00e0 degli Studi di Milano, Via Giovanni Celoria 16, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2100-6407","authenticated-orcid":false,"given":"Xavier","family":"Roca-Maza","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica \u201cAldo Pontremoli\u201d, Universit\u00e0 degli Studi di Milano, Via Giovanni Celoria 16, 20133 Milano, Italy"},{"name":"Istituto Nazionale di Fisica Nulceare, Sezione di Milano, Via Giovanni Celoria 16, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0819-1633","authenticated-orcid":false,"given":"Gianluca","family":"Col\u00f2","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica \u201cAldo Pontremoli\u201d, Universit\u00e0 degli Studi di Milano, Via Giovanni Celoria 16, 20133 Milano, Italy"},{"name":"Istituto Nazionale di Fisica Nulceare, Sezione di Milano, Via Giovanni Celoria 16, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1126\/science.1078070","article-title":"Determination of the Equation of State of Dense Matter","volume":"298","author":"Danielewicz","year":"2002","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10","DOI":"10.12942\/lrr-2008-10","article-title":"Physics of Neutron Star Crusts","volume":"11","author":"Chamel","year":"2008","journal-title":"Living Rev. Relativ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"L5","DOI":"10.1088\/2041-8205\/765\/1\/L5","article-title":"The Neutron Star Mass-Radius Relation and the Equation of State of Dense Matter","volume":"765","author":"Steiner","year":"2013","journal-title":"Astrophys. J. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1140\/epja\/i2014-14040-y","article-title":"Constraints on the symmetry energy using the mass-radius relation of neutron stars","volume":"50","author":"Lattimer","year":"2014","journal-title":"Eur. Phys. J. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"015007","DOI":"10.1103\/RevModPhys.89.015007","article-title":"Equations of state for supernovae and compact stars","volume":"89","author":"Oertel","year":"2017","journal-title":"Rev. Mod. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"103003","DOI":"10.1103\/PhysRevD.102.103003","article-title":"Effect of the crust on neutron star empirical relations","volume":"102","author":"Ferreira","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_7","unstructured":"Carreau, T. (2020). Modeling the (Proto)Neutron Star Crust: Toward a Controlled Estimation of Uncertainties. [Ph.D. Thesis, Normandie Universit\u00e9]."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2518","DOI":"10.1103\/PhysRevLett.61.2518","article-title":"Equation of State and the Maximum Mass of Neutron Stars","volume":"61","author":"Prakash","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1804","DOI":"10.1103\/PhysRevC.58.1804","article-title":"Equation of state of nucleon matter and neutron star structure","volume":"58","author":"Akmal","year":"1998","journal-title":"Phys. Rev. C"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"122501","DOI":"10.1103\/PhysRevLett.95.122501","article-title":"Neutron-Rich Nuclei and Neutron Stars: A New Accurately Calibrated Interaction for the Study of Neutron-Rich Matter","volume":"95","author":"Piekarewicz","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"161102","DOI":"10.1103\/PhysRevLett.105.161102","article-title":"Constraints on Neutron Star Radii Based on Chiral Effective Field Theory Interactions","volume":"105","author":"Hebeler","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"032801","DOI":"10.1103\/PhysRevC.85.032801","article-title":"Maximum mass and radius of neutron stars, and the nuclear symmetry energy","volume":"85","author":"Gandolfi","year":"2012","journal-title":"Phys. Rev. C"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"044305","DOI":"10.1103\/PhysRevC.90.044305","article-title":"Building relativistic mean field models for finite nuclei and neutron stars","volume":"90","author":"Chen","year":"2014","journal-title":"Phys. Rev. C"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"012031","DOI":"10.1088\/1742-6596\/668\/1\/012031","article-title":"Hyperons in Neutron Stars","volume":"668","year":"2016","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1038\/s41567-020-0914-9","article-title":"Evidence for quark-matter cores in massive neutron stars","volume":"16","author":"Annala","year":"2020","journal-title":"Nat. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.ppnp.2018.04.001","article-title":"Nuclear equation of state from ground and collective excited state properties of nuclei","volume":"101","author":"Paar","year":"2018","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1038\/nature11188","article-title":"The limits of the nuclear landscape","volume":"486","author":"Erler","year":"2012","journal-title":"Nature"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"A103","DOI":"10.1051\/0004-6361\/201526642","article-title":"Unified equation of state for neutron stars on a microscopic basis","volume":"584","author":"Sharma","year":"2015","journal-title":"Astron. Astrophys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/adnd.1997.0740","article-title":"Coulomb displacement energies between analog levels for 3<A<239","volume":"66","author":"Antony","year":"1997","journal-title":"At. Data Nucl. Data Tables"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1146\/annurev.ns.19.120169.002351","article-title":"Coulomb Energies","volume":"19","author":"Nolen","year":"1969","journal-title":"Annu. Rev. Nucl. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"202501","DOI":"10.1103\/PhysRevLett.120.202501","article-title":"Nuclear Symmetry Energy and the Breaking of the Isospin Symmetry: How Do They Reconcile with Each Other?","volume":"120","author":"Sagawa","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"122502","DOI":"10.1103\/PhysRevLett.102.122502","article-title":"Nuclear Symmetry Energy Probed by Neutron Skin Thickness of Nuclei","volume":"102","author":"Centelles","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.nuclphysa.2013.11.005","article-title":"Symmetry energy II: Isobaric analog states","volume":"922","author":"Danielewicz","year":"2014","journal-title":"Nucl. Phys. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"031306","DOI":"10.1103\/PhysRevC.86.031306","article-title":"New Skyrme interaction with improved spin-isospin properties","volume":"86","author":"Sagawa","year":"2012","journal-title":"Phys. Rev. C"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0370-2693(98)01499-3","article-title":"Isospin symmetry breaking nucleon-nucleon potentials and nuclear structure","volume":"445","author":"Muther","year":"1999","journal-title":"Phys. Lett. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"01002","DOI":"10.1051\/epjconf\/201819401002","article-title":"The nuclear symmetry energy and the breaking of the isospin symmetry: How do they reconcile with each other?","volume":"194","author":"Sagawa","year":"2018","journal-title":"EPJ Web Conf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1063\/1.4909560","article-title":"Introduction to neutron stars","volume":"1645","author":"Lattimer","year":"2015","journal-title":"AIP Conf. Proc."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/S0375-9474(97)00596-4","article-title":"A Skyrme parametrization from subnuclear to neutron star densities","volume":"627","author":"Chabanat","year":"1997","journal-title":"Nucl. Phys. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1855","DOI":"10.1103\/PhysRevC.19.1855","article-title":"Neutron isotopic density differences deduced from 0.8 GeV polarized proton elastic scattering","volume":"19","author":"Ray","year":"1979","journal-title":"Phys. Rev. C"},{"key":"ref_30","first-page":"607","article-title":"A coherent interpretation of the form factors of the nucleon in terms of a pion cloud and constituent quarks","volume":"17","author":"Friedrich","year":"2003","journal-title":"Eur. Phys. J. A Hadron. Nucl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"035009","DOI":"10.1103\/RevModPhys.88.035009","article-title":"CODATA recommended values of the fundamental physical constants: 2014","volume":"88","author":"Mohr","year":"2016","journal-title":"Rev. Mod. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.ppnp.2006.10.001","article-title":"Coulomb energy differences between high-spin states in isobaric multiplets","volume":"59","author":"Bentley","year":"2007","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/0370-2693(74)90617-0","article-title":"Coulomb exchange contribution in nuclear Hartree-Fock calculations","volume":"49","author":"Quentin","year":"1974","journal-title":"Phys. Lett. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"044313","DOI":"10.1103\/PhysRevC.94.044313","article-title":"Fully self-consistent study of charge-exchange resonances and the impact on the symmetry energy parameters","volume":"94","author":"Cao","year":"2016","journal-title":"Phys. Rev. C"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1103\/PhysRevA.13.1283","article-title":"Accurate and efficient methods for the evaluation of vacuum-polarization potentials of order Z\u03b1 and Z\u03b12","volume":"13","author":"Fullerton","year":"1976","journal-title":"Phys. Rev. A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0370-2693(95)00498-A","article-title":"Isospin mixing and the sum rule of super-allowed fermi beta decay","volume":"353","author":"Sagawa","year":"1995","journal-title":"Phys. Lett. B"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1140\/epja\/i2019-12923-y","article-title":"Collective excitations involving spin and isospin degrees of freedom","volume":"55","author":"Sagawa","year":"2019","journal-title":"Eur. Phys. J. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"R1360","DOI":"10.1103\/PhysRevC.47.R1360","article-title":"Charge independence and charge symmetry breaking interactions and the Coulomb energy anomaly in isobaric analog states","volume":"47","author":"Suzuki","year":"1993","journal-title":"Phys. Rev. C"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"054314","DOI":"10.1103\/PhysRevC.93.054314","article-title":"Asymmetric nuclear matter based on chiral two- and three-nucleon interactions","volume":"93","author":"Drischler","year":"2016","journal-title":"Phys. Rev. C"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"024305","DOI":"10.1103\/PhysRevC.93.024305","article-title":"Quantum Monte Carlo calculations of neutron matter with chiral three-body forces","volume":"93","author":"Tews","year":"2016","journal-title":"Phys. Rev. C"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1038\/nature09466","article-title":"A two-solar-mass neutron star measured using Shapiro delay","volume":"467","author":"Demorest","year":"2010","journal-title":"Nature"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1233232","DOI":"10.1126\/science.1233232","article-title":"A Massive Pulsar in a Compact Relativistic Binary","volume":"340","author":"Antoniadis","year":"2013","journal-title":"Science"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"L21","DOI":"10.3847\/2041-8213\/ab481c","article-title":"A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation","volume":"887","author":"Riley","year":"2019","journal-title":"Astrophys. J."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"L24","DOI":"10.3847\/2041-8213\/ab50c5","article-title":"PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter","volume":"887","author":"Miller","year":"2019","journal-title":"Astrophys. J."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"L22","DOI":"10.3847\/2041-8213\/ab451a","article-title":"A NICER View of PSR J0030+0451: Implications for the Dense Matter Equation of State","volume":"887","author":"Raaijmakers","year":"2019","journal-title":"Astrophys. J."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"161101","DOI":"10.1103\/PhysRevLett.119.161101","article-title":"GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral","volume":"119","author":"Abbott","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"L3","DOI":"10.3847\/2041-8213\/ab75f5","article-title":"GW190425: Observation of a Compact Binary Coalescence with Total Mass \u223c 3.4 M \u2299","volume":"892","author":"Abbott","year":"2020","journal-title":"Astrophys. J."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"084016","DOI":"10.1103\/PhysRevD.81.084016","article-title":"Effective one body description of tidal effects in inspiralling compact binaries","volume":"81","author":"Damour","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"172702","DOI":"10.1103\/PhysRevLett.120.172702","article-title":"Neutron Skins and Neutron Stars in the Multimessenger Era","volume":"120","author":"Fattoyev","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"091102","DOI":"10.1103\/PhysRevLett.121.091102","article-title":"Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817","volume":"121","author":"De","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"084018","DOI":"10.1103\/PhysRevD.80.084018","article-title":"Relativistic theory of tidal Love numbers","volume":"80","author":"Binnington","year":"2009","journal-title":"Phys. Rev. D"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/144\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:11:53Z","timestamp":1760159513000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/144"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,16]]},"references-count":51,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010144"],"URL":"https:\/\/doi.org\/10.3390\/sym13010144","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,1,16]]}}}