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EPJ Web of Conferences

Quantum shape phase transitions from spherical to deformed for Bose-Fermi systems: the effect of the odd particle around the critical point

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

Published Jan 1, 2014• 5 citations
Publisher

Abstract

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.

DOI
10.1051/epjconf/20146602014

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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 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.
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.
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
We study quantum phase transitions between spherical, prolate, and oblate nuclear ground-state shapes using the interacting sd\mathrm{sd}sd-boson model (sd(sd(sd-IBM) and demonstrate the analogy between the IBM results (also results of any axially symmetric quadrupole collective model) and predictions of the Landau theory of phase transitions in classical thermodynamics. A detailed comparison of the two frameworks is performed exploiting the concept of ``specific heat,'' introduced in four alternative ways in the quantum case. All these definitions (two of them based on spectroscopic features of the ground state, the others on a randomized version of the model) lead to similar peaked forms of the ``specific heat'' at the point of the quantum phase transition. We analyze the effect of an increasing boson number on these curves and observe convergence to the singular phase-transitional behavior in the classical limit. Other observable signatures of the IBM structural phase transitions are also discussed with the aim to facilitate the location of a particular nucleus in the parameter space (extended Casten triangle) near the transitions.
The quantum phase transitional behavior of an alternative characterization of the spherical to axially deformed shape-phase transition in the interacting boson model is explored. Specifically, the usual SU(3) quadrupole-quadrupole interaction is replaced by an O(6) cubic interaction, and the transitional behaviors of the low-lying energy levels, eigenstates, isomer shifts, $E$2 transition rates, and expectation values of shape variables across the entire transitional region are all examined within this context. A comparison with outcomes of the usual U(5)-SU(3) transitional description shows that the spherical to axially deformed shape-phase transition can also be described within this alternative context, especially near the critical point. However, with the O(6) cubic interaction the transition is considerably smoother than for the U(5)-SU(3) case, but with the nuclear shape less well defined, even in the axially deformed limit. It is also shown that the new scheme seems better than the usual U(5)-SU(3) scheme in describing the low-lying spectrum of 152{}^{152}152Sm with X(5) critical point symmetry.