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Physical Review Letters

Quantum Phase Transition for gamma-Soft Nuclei

Richard F. Casten, Jan Jolie, Peter von Brentano, Volker Werner

Published Jan 1, 2001• 72 citations
Publisher

Abstract

We examine a quantum phase transition in gamma-soft nuclei, where the O(6) limit is simultaneously a dynamical symmetry of the U(6) group of the interacting boson model and a critical point of a prolate-oblate phase transition. This is the only example of phase transitional behavior that can be described analytically for a finite s,d boson system.

DOI
10.17877/de290r-11105

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We examine a quantum phase transition in gamma-soft nuclei, where the O(6) limit is simultaneously a dynamical symmetry of the U(6) group of the interacting boson model and a critical point of a prolate-oblate phase transition. This is the only example of phase transitional behavior that can be described analytically for a finite s,d boson system.
We examine a quantum phase transition in $\ensuremath{\gamma}$-soft nuclei, where the O(6) limit is simultaneously a dynamical symmetry of the U(6) group of the interacting boson model and a critical point of a prolate-oblate phase transition. This is the only example of phase transitional behavior that can be described analytically for a finite s,ds,ds,d boson system.
We study the details of the U(3)--O(4) quantum phase transition in the U(4) vibron model. Both asymptotic analysis in the classical limit and rigorous calculations for finite boson number systems indicate that a second-order phase transition is still there even for the systems with boson number NNN ranging from tens to hundreds. Two kinds of effective order parameters, including E1E1E1 transition ratios $B(E1:{2}_{1}\ensuremath{\rightarrow}{1}_{1})/B(E1:{1}_{1}\ensuremath{\rightarrow}{0}_{1})$ and $B(E1:{0}_{2}\ensuremath{\rightarrow}{1}_{1})/B(E1:{1}_{1}\ensuremath{\rightarrow}{0}_{1})$, and the energy ratios E21/E02{E}_{{2}_{1}}/{E}_{{0}_{2}}E21​​/E02​​ and E31/E02{E}_{{3}_{1}}/{E}_{{0}_{2}}E31​​/E02​​ are proposed to identify the second-order phase transition in experiments. We also found that the critical point of phase transition can be approximately described by the E(3) symmetry, which persists even for moderate N 10N~10N 10 protected by the scaling behaviors of quantities at the critical point. In addition, a possible empirical example exhibiting roughly the E(3) symmetry is discussed.
Quantum phase transitional patterns in the whole parameter space of the consistent- Q Hamiltonian in the interacting boson model are studied based on an implemented Fortran code for the numerical computation of the matrix elements in the SU (3) Draayer–Akiyama basis. Results with respect to both ground and some excited states of the model Hamiltonian are discussed. Quantum phase transitional behavior in a variety of parameter situations is shown. It is found that transitional behavior of excited states is more complicated. Pt isotopes are taken as examples in illustrating the prolate–oblate shape phase transition.
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.