{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:36:51Z","timestamp":1760233011402,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,10]],"date-time":"2022-12-10T00:00:00Z","timestamp":1670630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12175097","12175066"],"award-info":[{"award-number":["12175097","12175066"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Based on the well-known rotor-vibrator model and the particle-plus-rotor model, multi-particle-hole excitations from a collective even-even core described by the rotor-vibrator is considered to describe well-deformed even-even nuclei. Like the particle-plus-rotor model, the intrinsic Vierergruppe (D2) symmetry is still preserved in the rotor-vibrator plus multi-particle-hole description. It is shown that a series of experimentally observed 0+ states in these nuclei may be interpreted as the multi-particle-hole excitations in a complementary manner to the beta and gamma vibrations described by the rotor-vibrator model. As a typical example of the model application, low-lying positive parity level energies below 1.990 MeV in the eight experimentally identified positive parity bands; a series of 0+ excitation energies up to 016+; and some experimentally known B(E2) values, E2 branching ratios, and E2\/M1 and E0\/E2 mixing ratios of 154Gd are fitted and compared to the experimental data. The results suggest that the multi-particle-hole-pair configuration mixing may play a role in these 0+ states.<\/jats:p>","DOI":"10.3390\/sym14122620","type":"journal-article","created":{"date-parts":[[2022,12,12]],"date-time":"2022-12-12T03:02:37Z","timestamp":1670814157000},"page":"2620","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Rotor-Vibrator Plus Multi-Particle-Hole Description of 154Gd"],"prefix":"10.3390","volume":"14","author":[{"given":"Yingxin","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}]},{"given":"Aoxue","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5118-1719","authenticated-orcid":false,"given":"Feng","family":"Pan","sequence":"additional","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8320-0651","authenticated-orcid":false,"given":"Lianrong","family":"Dai","sequence":"additional","affiliation":[{"name":"Department of Physics, School of Science, Huzhou University, Huzhou 313000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3568-8223","authenticated-orcid":false,"given":"Jerry","family":"Draayer","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,10]]},"reference":[{"key":"ref_1","unstructured":"Bohr, A., and Mottelson, B.R. (1975). Nuclear Structure II, Benjamin."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Iachello, F., and Arima, A. (1987). The Interacting Boson Model, Cambridge University.","DOI":"10.1017\/CBO9780511895517"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"092502","DOI":"10.1103\/PhysRevLett.99.092502","article-title":"Microscopic description of nuclear quantum phase transitions","volume":"99","author":"Vretenar","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.ppnp.2008.06.002","article-title":"Quantum phase transitions and structural evolution in nuclei","volume":"62","author":"Casten","year":"2009","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2155","DOI":"10.1103\/RevModPhys.82.2155","article-title":"Quantum phase transitions in the shapes of atomic nuclei","volume":"82","author":"Cejnar","year":"2010","journal-title":"Rev. Mod. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.physletb.2017.11.019","article-title":"Bohr model description of the critical point for the first order shape phase transition","volume":"776","author":"Budaca","year":"2018","journal-title":"Phys. Lett. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103891","DOI":"10.1016\/j.ppnp.2021.103891","article-title":"Quantum phase transitions in algebraic and collective models of nuclear structure","volume":"121","author":"Fortunato","year":"2021","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"B\u00f6y\u00fckata, M., Alonso, C.E., Arias, J.M., Fortunato, L., and Vitturi, A. (2021). Review of shape phase transition studies for Bose-Fermi systems: The effect of the odd-particle on the bosonic core. Symmetry, 13.","DOI":"10.3390\/sym13020215"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1103\/PhysRevC.57.1703","article-title":"Towards understanding magnetic dipole excitations in deformed nuclei: Phenomenology","volume":"57","author":"Rompf","year":"1998","journal-title":"Phys. Rev. C"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"054307","DOI":"10.1103\/PhysRevC.61.054307","article-title":"Scissors mode and the pseudo-SU(3) model","volume":"61","author":"Beuschel","year":"2000","journal-title":"Phys. Rev. C"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"064313","DOI":"10.1103\/PhysRevC.62.064313","article-title":"Shell model description of normal parity bands in even-even heavy deformed nuclei","volume":"62","author":"Popa","year":"2000","journal-title":"Phys. Rev. C"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1422","DOI":"10.1103\/PhysRevLett.51.1422","article-title":"Shell-model description of the low-energy structure of strongly deformed nuclei","volume":"51","author":"Draayer","year":"1983","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/0003-4916(84)90210-0","article-title":"Towards a shell model description of the low-energy structure of deformed nuclei I. Even-even systems","volume":"156","author":"Draayer","year":"1984","journal-title":"Ann. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/0003-4916(87)90047-9","article-title":"Towards a shell-model description of the low-energy structure of deformed nuclei II. Electromagnetic properties of collective M1 bands","volume":"180","author":"Draayer","year":"1987","journal-title":"Ann. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1071\/PH790307","article-title":"Dynamic deformation theory and multiphonon vibrational bands in l54Gd","volume":"32","author":"Kumar","year":"1979","journal-title":"Aust. J. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1088\/0954-3899\/31\/8\/018","article-title":"Coherent state description of the shape phase transition in even-even Gd isotopes","volume":"31","author":"Raduta","year":"2005","journal-title":"J. Phys. G Nucl. Part. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0003-4916(78)90228-2","article-title":"Interacting boson model of collective nuclear states II. The rotational limit","volume":"111","author":"Arima","year":"1978","journal-title":"Ann. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Casten, R.F. (2001). Nuclear Structure from a Simple Perspective, Oxford University. [2nd ed.].","DOI":"10.1093\/acprof:oso\/9780198507246.001.0001"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/0375-9474(82)90566-8","article-title":"An extension of the interacting boson model and its application to the even-even Gd isotope","volume":"380","author":"Heyde","year":"1982","journal-title":"Nucl. Phys. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1088\/0031-8949\/27\/1\/002","article-title":"Study of even Gd nuclei by decay of oriented Tb, with analysis by simple boson models","volume":"27","author":"Lipas","year":"1983","journal-title":"Phys. Scr."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/0370-2693(85)91573-4","article-title":"IBA consistent-Q formalism extended to the vibrational region","volume":"155","author":"Lipas","year":"1985","journal-title":"Phys. Lett. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1103\/PhysRevC.42.280","article-title":"Effective boson number calculations near the Z = 64 subshell","volume":"42","author":"Han","year":"1990","journal-title":"Phys. Rev. C"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"041302(R)","DOI":"10.1103\/PhysRevC.83.041302","article-title":"Microscopic formulation of the interacting boson model for rotational nuclei","volume":"83","author":"Nomura","year":"2011","journal-title":"Phys. Rev. C"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1103\/PhysRevLett.28.50","article-title":"Low-Lying 0+ states and (p,t) strengths in the actinides","volume":"28","author":"Kahana","year":"1972","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"R1","DOI":"10.1088\/0954-3899\/27\/1\/201","article-title":"Characterization of the \u03b2 vibration and 02+ states in deformed nuclei","volume":"27","author":"Garrett","year":"2001","journal-title":"J. Phys. G Nucl. Part. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1140\/epja\/i2011-11005-8","article-title":"Congruent band structures in 154Gd: Configuration-dependent pairing, a double vacuum and lack of \u03b2-vibrations","volume":"47","author":"Mullins","year":"2011","journal-title":"Eur. Phys. J. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1140\/epja\/i2011-11006-7","article-title":"Blocking of coupling to the 02+ excitation in 154Gd by the [505]11\/2\u2212 neutron in 155Gd","volume":"47","author":"Madiba","year":"2011","journal-title":"Eur. Phys. J. A"},{"key":"ref_28","unstructured":"Eisenberg, J.M., and Greiner, W. (1987). Nuclear Theory Vol. 1: Nuclear Models, North-Holland Publishing Co.. [3rd ed.]."},{"key":"ref_29","unstructured":"NuDat 2.8, National Nuclear Data Center (2022, October 05). Brookhaven National Laboratory, Available online: http:\/\/www.nndc.bnl.gov\/nudat2."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/0375-9474(81)90519-4","article-title":"On the particle-plus-rotor model","volume":"366","author":"Hilton","year":"1981","journal-title":"Nucl. Phys. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"044307","DOI":"10.1103\/PhysRevC.75.044307","article-title":"Chiral bands for a quasi-proton and quasi-neutron coupled with a triaxial rotor","volume":"75","author":"Zhang","year":"2007","journal-title":"Phys. Rev C"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"024327","DOI":"10.1103\/PhysRevC.88.024327","article-title":"Possible presence and properties of multi-chiral-pair bands in odd-odd nuclei with the same intrinsic configuration","volume":"88","author":"Hamamoto","year":"2013","journal-title":"Phys. Rev C"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"054309","DOI":"10.1103\/PhysRevC.96.054309","article-title":"Microscopic core-quasiparticle coupling model for spectroscopy of odd-mass nuclei","volume":"96","author":"Quan","year":"2017","journal-title":"Phys. Rev C"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1016\/j.physletb.2018.06.030","article-title":"Multiple chiral doublets in four-j shells particle rotor model: Five possible chiral doublets in 60136Nd76","volume":"782","author":"Chen","year":"2018","journal-title":"Phys. Lett. B"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/0029-5582(60)90191-7","article-title":"Rotation-vibration interaction in non-axial even nuclei","volume":"20","author":"Davydov","year":"1960","journal-title":"Nucl. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1142\/S0218301395000250","article-title":"Projected shell model and high-spin spectroscopy","volume":"4","author":"Hara","year":"1995","journal-title":"Int. J. Mod. Phys. E"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.nuclphysa.2018.09.001","article-title":"Microscopic description of structural evolution in Pd, Xe, Ba, Nd, Sm, Gd and Dy isotopes","volume":"979","author":"Naz","year":"2018","journal-title":"Nucl. Phys. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0370-2693(81)90321-X","article-title":"Configuration mixing in the interacting boson model","volume":"100","author":"Duval","year":"1981","journal-title":"Phys. Lett. B"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0375-9474(82)90061-6","article-title":"Quantitative description of configuration mixing in the interacting boson model","volume":"376","author":"Duval","year":"1982","journal-title":"Nucl. Phys. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.nuclphysa.2015.12.010","article-title":"Nuclear structure of 96,98Mo: Shape coexistence and mixed-symmetry states","volume":"947","author":"Thomas","year":"2016","journal-title":"Nucl. Phys. A"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/0370-2693(84)90023-6","article-title":"IBA-1 calculation of E2\/M1 mixing ratios in 154Gd","volume":"139B","author":"Lipas","year":"1984","journal-title":"Phys. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2257","DOI":"10.1016\/j.nds.2009.09.001","article-title":"Nuclear Data Sheets for A = 154","volume":"110","author":"Reich","year":"2009","journal-title":"Nucl. Data Sheets"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/S0375-9474(99)00143-8","article-title":"Electric monopole transitions from low energy excitations in nuclei","volume":"651","author":"Wood","year":"1999","journal-title":"Nucl. Phys. A"},{"key":"ref_44","first-page":"1","article-title":"Nuclear ground-state masses and deformations: FRDM(2012)","volume":"109\u2013110","author":"Sierk","year":"2016","journal-title":"At. Data Nucl. Data Tables"},{"key":"ref_45","unstructured":"Bidaman, H. (2017). A Study on Low Spin States in 154Gd Using the (p, p\u2032\u03b3) Reaction. [Master\u2019s Thesis, The University of Guelph]. Available online: https:\/\/atrium.lib.uoguelph.ca\/xmlui\/handle\/10214\/11590."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"102501","DOI":"10.1103\/PhysRevLett.91.102501","article-title":"Low-energy coexisting band in 154Gd","volume":"91","author":"Kulp","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.adt.2004.11.002","article-title":"Electric monopole transitions between 0+ states for nuclei throughout the periodic table","volume":"89","author":"Spear","year":"2005","journal-title":"At. Data Nucl. Data Tables"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1103\/RevModPhys.83.1467","article-title":"Shape coexistence in atomic nuclei","volume":"83","author":"Heyde","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1016\/0375-9474(70)90797-9","article-title":"A note on band mixing in 154Gd","volume":"153","author":"Keller","year":"1970","journal-title":"Nucl. Phys. A"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1140\/epja\/i2018-12617-0","article-title":"Band mixing in 154Gd","volume":"54","author":"Fortune","year":"2018","journal-title":"Eur. Phys. J. A"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1088\/0305-4616\/9\/7\/014","article-title":"Multipole mixing ratios of transitions in 154Gd","volume":"9","author":"Girit","year":"1983","journal-title":"J. Phys. G Nucl. Phys."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2620\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:55Z","timestamp":1760146675000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/12\/2620"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,10]]},"references-count":51,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["sym14122620"],"URL":"https:\/\/doi.org\/10.3390\/sym14122620","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,12,10]]}}}