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arXiv:nucl-th/0411015 · Physical Review Letters

Phase Structure of the Two-Fluid Proton-Neutron System

M. A. Caprio, FRANCESCO IACHELLO

Published Dec 10, 2004• 65 citations
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Abstract

The phase structure of a two-fluid bosonic system is investigated. The proton-neutron interacting boson model possesses a rich phase structure involving three control parameters and multiple order parameters. The surfaces of quantum phase transition between spherical, axially symmetric deformed, and SU(*)(pinu)(3) triaxial phases are determined.

DOI
10.1103/physrevlett.93.242502

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The phase structure of a two-fluid bosonic system is investigated. The proton-neutron interacting boson model possesses a rich phase structure involving three control parameters and multiple order parameters. The surfaces of quantum phase transition between spherical, axially symmetric deformed, and SU(*)(pinu)(3) triaxial phases are determined.
We study quasicritical phenomena in transitions between two "quantum phases" of a finite boson system, described by the interacting boson model 1 used in nuclear physics. The model is formulated in the algebraic framework and has a simple geometrical interpretation; the "phases" represented by dynamical symmetries U(5) and SU(3) correspond to spherical and deformed nuclear shapes. The quasicriticality of the U(5)-SU(3) transition is shown to be connected with the following phenomena simultaneously occurring in a narrow parameter region between the symmetries: (a) abrupt structural changes of eigenstates, (b) multiple avoided crossing of levels, (c) peaked density of exceptional points, (d) qualitative changes of the corresponding classical potential. We show that these spectroscopic features influence the dynamics of intersymmetry transitions in the model parameter space if the parameters themselves become dynamical variables.
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.
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.
We analyse the phase structure of a class of interacting boson models with two types of bosons, one scalar and one non-scalar, subject to one- and two-body interactions and with dynamic algebra U(n). To these models, we associate a classical description in terms of f = n − 1 variables. We show that, if the system is invariant under two- or three-dimensional rotations (for f ≥ 2 even or odd), the models have both first- and second-order phase transitions only if f = 5, 9, 13, .... In the other f ≥ 2 cases, the system has only second-order transitions. All phase transitions of this class of models belong to the cusp catastrophe in the classification of structurally unstable potentials.