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Öğe Erratum to: Unexpected transitional paths in the prolate to oblate shape phase transitions for Bose–Fermi systems (The European Physical Journal A, (2021), 57, 1, (2), 10.1140/epja/s10050-020-00308-4)(Springer Science and Business Media Deutschland GmbH, 2021) Böyükata, M.; Alonso, C.E.; Arias, J.M.; Fortunato, L.; Vitturi, A.This work was supported by the Scientific and Technical Research Council of Turkey (TÜB?ITAK), under the project number 119F127, by the Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (Spain) under Group FQM-160, by the Spanish Ministerio de Ciencia e Innovaciíon, ref. FIS2017-88410-P and PID2019-104002GB-C22, and by the European Commission, ref. H2020-INFRAIA-2014-2015 (ENSAR2). In the acknowledgments part of the published version of Eur. Phys. J. A 57 (2021) 2, the project number is corrected as 119F127. The original article can be found online at https:// doi.org/10.1140/epja/s10050-020-00308-4. © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021Öğe Odd nuclei and shape phase transitions: the role of the unpaired fermion(World Scientific Publ Co Pte Ltd, 2011) Fortunato, L.; Alonso, C. E.; Arias, J. M.; Boyukata, M.; Vitturi, A.Shape phase transitions in even and odd systems are reviewed within the frameworks of the Interacting Boson Model(IBM) and the Interacting Boson Fermion Model(IBFM), respectively and compared with geometric models when available. We discuss, in particular, the case of an odd j = 3/2 particle coupled to an even-even boson core that undergoes a transition from the spherical limit U(5) to the gamma-unstable limit O(6). Energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviors qualitatively similar to those of the even core and they agree qualitatively with the model based on the E(5/4) boson-fermion symmetry. We describe then the U-BF(5) to SUBF(3) transition when a fermion is allowed to occupy the orbits j = 1/2, 3/2,5/2. The additional particle characterizes the properties at the critical points in finite quantum systems.Öğe Review of Shape Phase Transition Studies for Bose-Fermi Systems: The Effect of the Odd-Particle on the Bosonic Core(Mdpi, 2021) Boyukata, M.; Alonso, C. E.; Arias, J. M.; Fortunato, L.; Vitturi, A.The quantum phase transition studies we have done during the last few years for odd-even systems are reviewed. The focus is on the quantum shape phase transition in Bose-Fermi systems. They are studied within the Interacting Boson-Fermion Model (IBFM). The geometry is included in this model by using the intrinsic frame formalism based on the concept of coherent states. First, the critical point symmetries E(5/4) and E(5/12) are summarized. E(5/4) describes the case of a single j = 3/2 particle coupled to a bosonic core that undergoes a transition from spherical to gamma-unstable. E(5/12) is an extension of E(5/4) that describes the multi-j case (j = 1/2,3/2,5/2) along the same transitional path. Both, E(5/4) and E(5/12), are formulated in a geometrical context using the Bohr Hamiltonian. Similar situations can be studied within the IBFM considering the transitional path from U-BF(5) to O-BF(6). Such studies are also presented. No critical points have been proposed for other paths in odd-even systems as, for instance, the transition from spherical to axially deformed shapes. However, the study of such shape phase transition can be done easily within the IBFM considering the path from U-BF(5) (spherical) to SUBF(3) (axial deformed). Thus, in a second part, this study is presented for the multi-j case. Energy levels and potential energy surfaces obtained within the intrinsic frame formalism of the IBFM Hamiltonian are discussed. Finally, our recent works within the IBFM for a single-j fermion coupled to a bosonic core that performs different shape phase transitional paths are reviewed. All significant paths in the model space are studied: from spherical to gamma-unstable shape, from spherical to axially deformed (prolate and oblate) shapes, and from prolate to oblate shape passing through the gamma-unstable shape. The aim of these applications is to understand the effect of the coupled fermion on the core when moving along a given transitional path and how the coupled fermion modifies the bosonic core around the critical points.Öğe Shape phase transition in odd-even nuclei: From spherical to deformed γ -unstable shapes(Amer Physical Soc, 2010) Böyükata, M.; Alonso, C. E.; Arias, J. M.; Fortunato, L.; Vitturi, A.Shape phase transitions in odd-A nuclei are investigated within the framework of the interacting boson-fermion model. The case of a single j = 9/2 fermion coupled to an even-even boson core is considered. This boson core transits from spherical to gamma-unstable shapes depending on the value of a control parameter in the boson Hamiltonian. The effect of the coupling of the odd particle to this core along the shape transition and, in particular, at the critical point is discussed. For that purpose, the ground-state energy surface in terms of the beta and gamma shape variables for the even core and odd-even energy surfaces for the different K states coming from j = 9/2 are constructed. The evolution of each individual coupled state along the transition from the spherical [U(5)] to the gamma-unstable [O(6)] situation is investigated. One finds that the core-fermion coupling gives rise to a smoother transition than in the even-core case.Öğe Unexpected transitional paths in the prolate to oblate shape phase transitions for Bose-Fermi systems (vol 57, 2, 2021)(Springer, 2021) Boyukata, M.; Alonso, C. E.; Arias, J. M.; Fortunato, L.; Vitturi, A.[Abstract No tAvailable]
