{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T04:53:58Z","timestamp":1772168038157,"version":"3.50.1"},"reference-count":59,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T00:00:00Z","timestamp":1676764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12275369"],"award-info":[{"award-number":["12275369"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12141501"],"award-info":[{"award-number":["12141501"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22qntd3101"],"award-info":[{"award-number":["22qntd3101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021B0301030006"],"award-info":[{"award-number":["2021B0301030006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities, Sun Yat-sen University","award":["12275369"],"award-info":[{"award-number":["12275369"]}]},{"name":"Fundamental Research Funds for the Central Universities, Sun Yat-sen University","award":["12141501"],"award-info":[{"award-number":["12141501"]}]},{"name":"Fundamental Research Funds for the Central Universities, Sun Yat-sen University","award":["22qntd3101"],"award-info":[{"award-number":["22qntd3101"]}]},{"name":"Fundamental Research Funds for the Central Universities, Sun Yat-sen University","award":["2021B0301030006"],"award-info":[{"award-number":["2021B0301030006"]}]},{"name":"Guangdong Major Project of Basic and Applied Basic Research","award":["12275369"],"award-info":[{"award-number":["12275369"]}]},{"name":"Guangdong Major Project of Basic and Applied Basic Research","award":["12141501"],"award-info":[{"award-number":["12141501"]}]},{"name":"Guangdong Major Project of Basic and Applied Basic Research","award":["22qntd3101"],"award-info":[{"award-number":["22qntd3101"]}]},{"name":"Guangdong Major Project of Basic and Applied Basic Research","award":["2021B0301030006"],"award-info":[{"award-number":["2021B0301030006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We explore the correlation of the neutrinoless double-\u03b2 decay nuclear matrix element (NME) with electric quadrupole (E2) strength in the framework of the Hamiltonian-based generator-coordinate method, which is a configuration-mixing calculation of symmetry-restored intrinsic basis states. The restoration of symmetries that are simultaneously broken in the mean-field states allows us to compute the structural and decay properties associated with wave functions characterized by good quantum numbers. Our calculations show a clear anti-correlation between the neutrinoless double-\u03b2 decay NME and the transition rate of the collective quadrupole excitation from the ground state in response to artificial changes of the quadrupole\u2013quadrupole interaction. The anti-correlation is more remarkable in the decay from a weakly deformed parent nucleus to a more deformed grand-daughter nucleus. This interrelation may provide a way to reduce the uncertainty of the nuclear matrix element.<\/jats:p>","DOI":"10.3390\/sym15020552","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T04:58:23Z","timestamp":1676869103000},"page":"552","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Correlation of Neutrinoless Double-\u03b2 Decay Nuclear Matrix Element with E2 Strength"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5292-5158","authenticated-orcid":false,"given":"Changfeng","family":"Jiao","sequence":"first","affiliation":[{"name":"School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3495-3614","authenticated-orcid":false,"given":"Cenxi","family":"Yuan","sequence":"additional","affiliation":[{"name":"Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9505-1852","authenticated-orcid":false,"given":"Jiangming","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1103\/RevModPhys.80.481","article-title":"Double beta decay, Majorana neutrinos, and neutrino mass","volume":"80","author":"Avignone","year":"2008","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"052503","DOI":"10.1103\/PhysRevLett.100.052503","article-title":"Influence of Pairing on the Nuclear Matrix Elements of the Neutrinoless \u03b2\u03b2 Decays","volume":"100","author":"Caurier","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.nuclphysa.2008.12.005","article-title":"Disassembling the nuclear matrix elements of the neutrinoless \u03b2\u03b2 decay","volume":"818","author":"Poves","year":"2009","journal-title":"Nucl. Phys. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"024321","DOI":"10.1103\/PhysRevC.81.024321","article-title":"Shell model analysis of the neutrinoless double-\u03b2 decay of 48Ca","volume":"81","author":"Horoi","year":"2010","journal-title":"Phys. Rev. C"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"014320","DOI":"10.1103\/PhysRevC.87.014320","article-title":"Shell model analysis of competing contributions to the double-\u03b2 decay of 48Ca","volume":"87","author":"Horoi","year":"2013","journal-title":"Phys. Rev. C"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"222502","DOI":"10.1103\/PhysRevLett.110.222502","article-title":"Shell-Model Analysis of the 136Xe Double Beta Decay Nuclear Matrix Elements","volume":"110","author":"Horoi","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"024309","DOI":"10.1103\/PhysRevC.91.024309","article-title":"Shell model studies of the 130Te neutrinoless double-\u03b2 decay","volume":"91","author":"Neacsu","year":"2015","journal-title":"Phys. Rev. C"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"024308","DOI":"10.1103\/PhysRevC.93.024308","article-title":"Shell model predictions for 124Sn double-\u03b2 decay","volume":"93","author":"Horoi","year":"2016","journal-title":"Phys. Rev. C"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"112502","DOI":"10.1103\/PhysRevLett.116.112502","article-title":"Large-Scale Shell-Model Analysis of the Neutrinoless \u03b2\u03b2 Decay of 48Ca","volume":"116","author":"Iwata","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"044334","DOI":"10.1103\/PhysRevC.93.024308","article-title":"Shell-model calculation of neutrinoless double-\u03b2 decay of 76Ge","volume":"93","author":"Horoi","year":"2016","journal-title":"Phys. Rev. C"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"042501","DOI":"10.1103\/PhysRevLett.109.042501","article-title":"Limits on Neutrino Masses from Neutrinoless Double-\u03b2 Decay","volume":"109","author":"Barea","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"014315","DOI":"10.1103\/PhysRevC.87.014315","article-title":"Nuclear matrix elements for double-\u03b2 decay","volume":"87","author":"Barea","year":"2013","journal-title":"Phys. Rev. C"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"034304","DOI":"10.1103\/PhysRevC.91.034304","article-title":"0\u03bd\u03b2\u03b2 and 2\u03bd\u03b2\u03b2 nuclear matrix elements in the interacting boson model with isospin restoration","volume":"91","author":"Barea","year":"2015","journal-title":"Phys. Rev. C"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"055502","DOI":"10.1103\/PhysRevC.60.055502","article-title":"Additional nucleon current contributions to neutrinoless double \u03b2 decay","volume":"60","author":"Pantis","year":"1999","journal-title":"Phys. Rev. C"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"044302","DOI":"10.1103\/PhysRevC.68.044302","article-title":"Uncertainty in the 0\u03bd\u03b2\u03b2 decay nuclear matrix elements","volume":"68","author":"Rodin","year":"2003","journal-title":"Phys. Rev. C"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.physletb.2007.01.054","article-title":"Short-range correlations and neutrinoless double beta decay","volume":"647","author":"Kortelainen","year":"2007","journal-title":"Phys. Lett. B"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"051303","DOI":"10.1103\/PhysRevC.75.051303","article-title":"Improved short-range correlations and 0\u03bd\u03b2\u03b2 nuclear matrix elements of 76Ge and 82Se","volume":"75","author":"Kortelainen","year":"2007","journal-title":"Phys. Rev. C"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"045503","DOI":"10.1103\/PhysRevC.77.045503","article-title":"Anatomy of the 0\u03bd\u03b2\u03b2 nuclear matrix elements","volume":"77","author":"Faessler","year":"2008","journal-title":"Phys. Rev. C"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"055501","DOI":"10.1103\/PhysRevC.79.055501","article-title":"0\u03bd\u03b2\u03b2-decay nuclear matrix elements with self-consistent short-range correlations","volume":"79","author":"Faessler","year":"2009","journal-title":"Phys. Rev. C"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"015502","DOI":"10.1103\/PhysRevC.79.015502","article-title":"0\u03bd\u03b2\u03b2 nuclear matrix elements and the occupancy of individual orbits","volume":"79","author":"Faessler","year":"2009","journal-title":"Phys. Rev. C"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"064302","DOI":"10.1103\/PhysRevC.87.064302","article-title":"Large-scale calculations of the double-\u03b2 decay of 76Ge,130Te,136Xe, and 150Nd in the deformed self-consistent Skyrme quasiparticle random-phase approximation","volume":"87","author":"Mustonen","year":"2013","journal-title":"Phys. Rev. C"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"045501","DOI":"10.1103\/PhysRevC.87.045501","article-title":"0\u03bd\u03b2\u03b2 and 2\u03bd\u03b2\u03b2 nuclear matrix elements, quasiparticle random-phase approximation, and isospin symmetry restoration","volume":"87","author":"Rodin","year":"2013","journal-title":"Phys. Rev. C"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"096010","DOI":"10.1103\/PhysRevD.90.096010","article-title":"Arbitrary mass Majorana neutrinos in neutrinoless double beta decay","volume":"90","author":"Faessler","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"024613","DOI":"10.1103\/PhysRevC.91.024613","article-title":"Nuclear matrix elements for 0\u03bd\u03b2\u03b2 decays with light or heavy Majorana-neutrino exchange","volume":"91","author":"Suhonen","year":"2015","journal-title":"Phys. Rev. C"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"045503","DOI":"10.1103\/PhysRevC.97.045503","article-title":"0\u03bd\u03b2\u03b2-decay nuclear matrix element for light and heavy neutrino mass mechanisms from deformed quasiparticle random-phase approximation calculations for 76Ge,82Se,130Te,136Xe, and 150Nd with isospin restoration","volume":"97","author":"Fang","year":"2018","journal-title":"Phys. Rev. C"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"252503","DOI":"10.1103\/PhysRevLett.105.252503","article-title":"Energy Density Functional Study of Nuclear Matrix Elements for Neutrinoless \u03b2\u03b2 Decay","volume":"105","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"142501","DOI":"10.1103\/PhysRevLett.111.142501","article-title":"Shape and Pairing Fluctuation Effects on Neutrinoless Double Beta Decay Nuclear Matrix Elements","volume":"111","author":"Vaquero","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.physletb.2012.12.063","article-title":"Neutrinoless \u03b2\u03b2 decay nuclear matrix elements in an isotopic chain","volume":"719","year":"2013","journal-title":"Phys. Lett. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"024316","DOI":"10.1103\/PhysRevC.91.024316","article-title":"Systematic study of nuclear matrix elements in neutrinoless double-\u03b2 decay with a beyond-mean-field covariant density functional theory","volume":"91","author":"Yao","year":"2015","journal-title":"Phys. Rev. C"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"014306","DOI":"10.1103\/PhysRevC.94.014306","article-title":"Octupole correlations in low-lying states of 150Nd and 150Sm and their impact on neutrinoless double-\u03b2 decay","volume":"94","author":"Yao","year":"2016","journal-title":"Phys. Rev. C"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"031301","DOI":"10.1103\/PhysRevC.90.031301","article-title":"Proton-neutron pairing amplitude as a generator coordinate for double-\u03b2 decay","volume":"90","author":"Hinohara","year":"2014","journal-title":"Phys. Rev. C"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"054310","DOI":"10.1103\/PhysRevC.96.054310","article-title":"Neutrinoless double-\u03b2 decay matrix elements in large shell-model spaces with the generator-coordinate method","volume":"96","author":"Jiao","year":"2017","journal-title":"Phys. Rev. C"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"064324","DOI":"10.1103\/PhysRevC.98.064324","article-title":"Neutrinoless double-\u03b2 decay of 124Sn, 130Te, and 136Xe in the Hamiltonian-based generator-coordinate method","volume":"98","author":"Jiao","year":"2018","journal-title":"Phys. Rev. C"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"031303","DOI":"10.1103\/PhysRevC.100.031303","article-title":"Union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-\u03b2 decay","volume":"100","author":"Jiao","year":"2019","journal-title":"Phys. Rev. C"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"232501","DOI":"10.1103\/PhysRevLett.124.232501","article-title":"Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of 48Ca","volume":"124","author":"Yao","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"182502","DOI":"10.1103\/PhysRevLett.126.182502","article-title":"Coupled-Cluster Calculations of Neutrinoless Double-\u03b2 Decay in 48Ca","volume":"126","author":"Novario","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"046301","DOI":"10.1088\/1361-6633\/aa5bc5","article-title":"Status and future of nuclear matrix elements for neutrinoless double-beta decay: A review","volume":"80","author":"Engel","year":"2017","journal-title":"Rep. Prog. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"124002","DOI":"10.1088\/0954-3899\/39\/12\/124002","article-title":"Nuclear structure and double beta decay","volume":"39","author":"Vogel","year":"2012","journal-title":"J. Phys. G Nucl. Part. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"103965","DOI":"10.1016\/j.ppnp.2022.103965","article-title":"Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism","volume":"126","author":"Yao","year":"2022","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1140\/epja\/i2007-10527-x","article-title":"Nuclear-structure aspects of the neutrinoless \u03b2\u03b2-decays","volume":"36","author":"Caurier","year":"2008","journal-title":"Eur. Phys. J. A"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"034320","DOI":"10.1103\/PhysRevC.83.034320","article-title":"Neutrinoless double-\u03b2 decay of deformed nuclei within quasiparticle random-phase approximation with a realistic interaction","volume":"83","author":"Fang","year":"2011","journal-title":"Phys. Rev. C"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"044319","DOI":"10.1103\/PhysRevC.96.044319","article-title":"Nuclear structure features of Gamow-Teller excitations","volume":"96","author":"Zelevinsky","year":"2017","journal-title":"Phys. Rev. C"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"054302","DOI":"10.1103\/PhysRevC.106.054302","article-title":"Statistical analysis for the neutrinoless double-\u03b2-decay matrix element of 48Ca","volume":"106","author":"Horoi","year":"2022","journal-title":"Phys. Rev. C"},{"key":"ref_44","first-page":"263","article-title":"Advances in Nuclear Physics","volume":"Volume 11","author":"Negele","year":"1979","journal-title":"Advances in Nuclear Physics"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Ring, P., and Schuck, P. (1980). The Nuclear Many-Body Problem, Springer.","DOI":"10.1007\/978-3-642-61852-9"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"064323","DOI":"10.1103\/PhysRevC.81.064323","article-title":"Triaxial angular momentum projection and configuration mixing calculations with the Gogny force","volume":"81","author":"Egido","year":"2010","journal-title":"Phys. Rev. C"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"044311","DOI":"10.1103\/PhysRevC.81.044311","article-title":"Configuration mixing of angular-momentum-projected triaxial relativistic mean-field wave functions","volume":"81","author":"Yao","year":"2010","journal-title":"Phys. Rev. C"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/S0375-9474(01)00967-8","article-title":"Shell model study of the isobaric chains A = 50, A = 51 and A = 52","volume":"694","author":"Poves","year":"2001","journal-title":"Nucl. Phys. A"},{"key":"ref_49","unstructured":"Gniady, A., Caurier, E., and Nowacki, F. (unpublised)."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"044323","DOI":"10.1103\/PhysRevC.86.044323","article-title":"Monopole-optimized effective interaction for tin isotopes","volume":"86","author":"Qi","year":"2012","journal-title":"Phys. Rev. C"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1103\/RevModPhys.77.427","article-title":"The shell model as a unified view of nuclear structure","volume":"77","author":"Caurier","year":"2005","journal-title":"Rev. Mod. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.adt.2015.10.001","article-title":"Tables of E2 transition probabilities from the first 2+ states in even\u2013even nuclei","volume":"107","author":"Pritychenko","year":"2016","journal-title":"At. Data Nucl. Data Tables"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"142501","DOI":"10.1103\/PhysRevLett.113.142501","article-title":"Nonperturbative Shell-Model Interactions from the In-Medium Similarity Renormalization Group","volume":"113","author":"Bogner","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"096302","DOI":"10.1088\/0034-4885\/77\/9\/096302","article-title":"Coupled-cluster computations of atomic nuclei","volume":"77","author":"Hagen","year":"2014","journal-title":"Rep. Prog. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"051301","DOI":"10.1103\/PhysRevC.93.051301","article-title":"Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians","volume":"93","author":"Stroberg","year":"2016","journal-title":"Phys. Rev. C"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"032502","DOI":"10.1103\/PhysRevLett.118.032502","article-title":"Nucleus-Dependent Valence-Space Approach to Nuclear Structure","volume":"118","author":"Stroberg","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"011301","DOI":"10.1103\/PhysRevC.94.011301","article-title":"Open sd-shell nuclei from first principles","volume":"94","author":"Jansen","year":"2016","journal-title":"Phys. Rev. C"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/0375-9474(88)90313-2","article-title":"0+\u21922+ neutrinoless \u03b2\u03b2 decay of 76Ge","volume":"484","author":"Tomoda","year":"1988","journal-title":"Nucl. Phys. A"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"045501","DOI":"10.1103\/PhysRevC.103.045501","article-title":"Nuclear matrix elements for the 0\u03bd\u03b2\u03b2(0+\u21922+) decay of 76Ge within the two-nucleon mechanism","volume":"103","author":"Fang","year":"2021","journal-title":"Phys. Rev. C"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/552\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:36:21Z","timestamp":1760121381000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,19]]},"references-count":59,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["sym15020552"],"URL":"https:\/\/doi.org\/10.3390\/sym15020552","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,19]]}}}