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Bulletin of the American Physical Society

Evolution of shape phase transitions as functions of energy, spin, and boson number in the Interacting Boson Model

Elizabeth T. Williams, R. J. Casperson, Volker Werner

Published Oct 27, 2006• 0 citations
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Physical Review C•Jun 10, 2008•14 citations
The evolution of system observables at critical points of quantum phase transitions in atomic nuclei is explored within the context of the interacting boson model-1. The evolution of energies and transition strengths in the ground state band at the infinite-size critical point are examined with respect to system size. Properties of first-order phase transitions away from the U(5)-SU(3) leg of the Casten triangle are examined, and the effects of angular momentum on the evolution of system observables at the critical point are investigated for the first time.
We study the energy level statistics of the states in U(5) and O(6) dynamical symmetries of the interacting boson model and the high spin states with backbending in U(5) symmetry. In the calculations, the degeneracy resulting from the additional quantum number is eliminated manually. The calculated results indicate that the finite boson number N effect is prominent. When N has a value close to a realistic one, increasing the interaction strength of subgroup O(5) makes the statistics vary from Poisson type to Gaussian orthogonal ensemble type and further recover to Poisson type. However, in the case of $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ they all tend to be Poisson type. The fluctuation property of the energy levels with backbending in high spin states in U(5) symmetry involves a signal of shape-phase transition between spherical vibration and axial rotation.
A study of first and second order nuclear shape phase transitional behavior in yrast states of even-even nuclei in the context of the Interacting Boson Model-1 is presented. Finite boson number effects are identified using calculations with up to 150 bosons, and the role of the rotational degree of freedom of observables in first and second order quantum phase transitional nuclei is discussed. We aim to provide a first investigation of the angular momentum dependence of experimentally accessible phase transitional signatures in finite-sized quantum nuclear systems.