scholarly journals Line of approximate SU(3) symmetry inside the symmetry triangle of the Interacting Boson Model

2020 ◽  
Vol 19 ◽  
pp. 16
Author(s):  
D. Bonatsos ◽  
S. Karampagia ◽  
R. F. Casten
Keyword(s):  
Phase Transition ◽  
Critical Line ◽  
Interacting Boson Model ◽  
Rigid Rotator ◽  
Symmetry Line ◽  
First Order ◽  
Boson Number ◽  
Boson Model ◽  
Shape Phase Transition ◽  
First Time

The U(5), SU(3), and O(6) symmetries of the Interacting Boson Model (IBM) have been traditionally placed at the vertices of the symmetry triangle, while an O(5) symmetry is known to hold along the U(5)–O(6) side of the triangle. We construct [1] for the first time a symmetry line in the interior of the triangle, along which the SU(3) symmetry is preserved. This is achieved by using the contraction of the SU(3) algebra to the algebra of the rigid rotator in the large boson number limit of the IBM. The line extends from the SU(3) vertex to near the critical line of the first order shape/phase transition separating the spherical and prolate deformed phases. It lies within the Alhassid–Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices amidst chaotic regions, thus providing an explanation for its existence.

scholarly journals What can we learn from the Interacting Boson Model in the limit of large boson numbers?

2020 ◽  
Vol 16 ◽  
pp. 1
Author(s):  
D. Bonatsos ◽  
E. A. McCutchan ◽  
R. F. Casten
Keyword(s):  
Ordinal Number ◽  
Interacting Boson Model ◽  
Valence Nucleon ◽  
First Order ◽  
Effective Order ◽  
Boson Number ◽  
Boson Model ◽  
Special Solutions ◽  
Shape Phase Transition ◽  
Boson Approximation

Over the years, studies of collective properties of medium and heavy mass nuclei in the framework of the Interacting Boson Approximation (IBA) model have focused on finite boson numbers, corresponding to valence nucleon pairs in specific nuclei. Attention to large boson numbers has been motivated by the study of shape/phase transitions from one limiting symmetry of IBA to another, which become sharper in the large boson number limit, revealing in parallel regularities previously unnoticed, although they survive to a large extent for finite boson numbers as well. Several of these regularities will be discussed. It will be shown that in all of the three limiting symmetries of the IBA [U(5), SU(3), and O(6)], energies of 0+ states grow linearly with their ordinal number. Furthermore, it will be proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(0^+_2 ) = E(6^+_1 ), E(0^+_3 ) = E(10^+_1 ), E(0^+_4 ) = E(14^+_1 ), the energy ratio E(6^+_1 )/E(0^+_2 ) turning out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first- and second-order transitions. The energies of 0+ states near the point of the first order shape/phase transition between U(5) and SU(3) will be shown to grow as n(n+3), where n is their ordinal number, in agreement with the rule dictated by the relevant critical point symmetries studied in the framework of special solutions of the Bohr Hamiltonian. The underlying dynamical and quasi-dynamical symmetries are also discussed.

scholarly journals Connecting the X(5)-β2, X(5)-β4, and X(3) models to the shape/phase transition region of the Interacting Boson Model

2020 ◽  
Vol 15 ◽  
pp. 118
Author(s):  
E. A. McCutchan ◽  
D. Bonatsos ◽  
R. F. Casten
Keyword(s):  
Phase Transition ◽  
Transition Region ◽  
Interacting Boson Model ◽  
Shape Transition ◽  
Scale Factors ◽  
Phase Transition Region ◽  
Boson Model ◽  
Shape Phase Transition ◽  
Two Parameter ◽  
Boson Approximation

The parameter independent (up to overall scale factors) predictions of the X(5)-β2, X(5)-β4, and X(3) models, which are variants of the X(5) critical point symmetry developed within the framework of the geometric collective model, are compared to two- parameter calculations in the framework of the interacting boson approximation (IBA) model. The results show that these geometric models coincide with IBA parameters consistent with the phase/shape transition region of the IBA for boson numbers of physical interest (close to 10). 186Pt and 172Os are identified as good examples of X(3), while 146Ce, 174Os and 158Er, 176Os are identified as good examples of X(5)-β2 and X(5)-β4 behavior respectively.

ROTATIONAL DRIVEN NUCLEAR SHAPE PHASE TRANSITION OF THE YRAST STATES OF INDIVIDUAL NUCLEUS IN INTERACTING BOSON MODEL

2006 ◽  
Vol 15 (08) ◽  
pp. 1711-1721 ◽  
Author(s):  
YUE ZHAO ◽  
YANG LIU ◽  
LIANG-ZHU MU ◽  
YU-XIN LIU
Keyword(s):  
Phase Transition ◽  
Angular Momentum ◽  
Interaction Parameters ◽  
Interacting Boson Model ◽  
Angular Momentum Projection ◽  
Prolate Shape ◽  
Boson Model ◽  
Shape Phase Transition ◽  
Nuclear Shape Phase Transition ◽  
Special Region

With the intrinsic coherent state formalism and the angular momentum projection, we study the shape phase structure of the yrast states in the dynamical symmetries of the IBM. We found that the states in the U (5) symmetry can undergo a rotation driven vibrational to axially rotational shape phase transition if the interaction parameters take negative values smaller than the critical ones. It shows that the U (5) symmetry of the IBM1 is an appropriate approach to describe the rotation driven shape phase transition along the yrast line of individual nucleus as the interaction parameters are taken in a special region. The O (6) symmetric yrast states may involve a phase transition from γ-soft rotation to triaxial rotation as the angular momentum increases, if the interaction parameters are specially chosen. And the yrast states in SU (3) symmetry always appear in the axially prolate shape phase.

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