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Journal of Physics Conference Series

Quantum phase transitions in odd-A nuclei: The effect of the odd particle from spherical to oblate shapes

Mahmut Böyükata, Clara E. Alonso, J. M. Arias, L. Fortunato, A. Vitturi

Published Feb 9, 2015• 7 citations
Publisher

Abstract

Quantum shape-phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model (IBFM). We consider the case of a single-j fermion coupled to an even-even boson core that performs a transition from spherical to oblate shapes varying a control parameter in the boson Hamiltonian. The aim of this work is to see the effect of the coupling of the unpaired fermion on the transition, to understand how the coupled single particle modifies the geometric shape of the system and how each of the odd states behaves when the boson core shifts along the transitional path.

DOI
10.1088/1742-6596/580/1/012047

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Quantum shape-phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model (IBFM). We consider the case of a single-j fermion coupled to an even-even boson core that performs a transition from spherical to oblate shapes varying a control parameter in the boson Hamiltonian. The aim of this work is to see the effect of the coupling of the unpaired fermion on the transition, to understand how the coupled single particle modifies the geometric shape of the system and how each of the odd states behaves when the boson core shifts along the transitional path.
Quantum phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model with a description based on the concept of intrinsic states. We consider the case of a single j=9/2 odd-particle coupled to an even-even boson core that performs a transition from spherical to deformed prolate and to deformed gamma-unstable shapes varying a control parameter in the boson Hamiltonian. The effect of the coupling of the odd particle to this core is discussed along the shape transition and, in particular, at the critical point.
Quantum phase transitions in even-even nuclei been extensively studied both in theory and experiment in the recent years. Odd-even nuclei can be considered as examples of mixed Bose-Fermi systems with a single fermion coupled to an even-even core. The eÆect of a fermion with angular momentum j on quantum phase transi- tions of a bosonic system comprised of s (L=0) and d (L=2) bosons is investigated. The analysis is based on an Interacting Boson Fermion Model (IBFM) Hamiltonian and its classical limit and it demostrates the changes in the energy level structure as well as the classical and quantum order parameters involved. Some experimental evidence is also presented and compared with theoretical calculations
In this paper‎, ‎we study the nature of the dynamics in second-order Quantum Phase Transition (QPT) between vibrational ( ) and -unstable ( ) nuclear shapes‎. ‎Using a transitional Hamiltonian according to an affine SU(1,1) algebra in combination with a coherent state formalism, Shape Phase Transitions (SPT) in odd-nuclei in the framework of the Interacting Boson Fermion Model (IBFM) are investigated‎. ‎Classical analysis reveals a change in the system along with the transition in a critical point‎. ‎The role of a fermion with angular momentum j at the critical point on quantum phase transitions in bosonic systems is investigated via a semi-classical approach‎. ‎The effect of the coupling of the odd particle to an even-even boson core is discussed along with the shape transition and‎, ‎in particular‎, ‎at the critical point‎. Our study confirms the importance of the odd nuclei as necessary signatures to characterize the occurrence of the phase transition and determine the critical point's precise position‎.
Background: One of the fundamental problems of quantum information science is quantum entanglement. Recently, quantum phase transition in nuclear systems is studied in connection with quantum entanglement.Purpose: In this paper, the use of entanglement entropy as a suitable signal for the study of quantum phase transition in the even-even and odd-AAA nuclei is investigated. The effect of the coupling of a single fermion to a boson core on entanglement entropy is studied.Method: By use of the affine SU(1,1)SU(1,1)SU(1,1) Lie algebra and through the Schmidt decomposition in the framework of the interacting boson model (IBM) and interacting boson-fermion model (IBFM), entanglement entropy in the even-even and odd-AAA are obtained. The entanglement entropy is used for tracking and studying the shape phase transition in these nuclei.Results: The entanglement entropy in the IBM and the IBFM is calculated. The entanglement entropy values of the low-lying states of 122−−134Xe,102−−110Pd^{122--134}\mathrm{Xe}, ^{102--110}\mathrm{Pd}122−−134Xe,102−−110Pd, and 123−−133Xe^{123--133}\mathrm{Xe}123−−133Xe were calculated and analyzed. It is found that entanglement entropy is a suitable order parameter to detect shape phase transition in nuclear systems.Conclusions: The obtained results indicate that the entropy of entanglement is sensitive to the shape-phase transition between spherical and $\ensuremath{\gamma}$-unstable regions in nuclei. The results show that entanglement entropy is a powerful tool for identifying shape phase transitions in nuclei. It is found that the coupling of the single fermion with angular momentum jjj to the even-even system does not change the geometry imposed by the boson core performing the transition and only the entanglement entropy values have been shifted by the addition of the odd particle with respect to the even case.
Quantum phase transitions (QPTs) in odd-mass Nb isotopes are investigated in the framework of the interacting boson-fermion model with configuration mixing. A quantum analysis reveals a Type I QPT (gradual shape-evolution within the intruder configuration) superimposed on a Type II QPT (abrupt crossing of normal and intruder states), thus demonstrating the occurrence of intertwined QPTs. A classical analysis highlights the implications for the single particle motion in the deformed field generated by the even-even Zr cores.