Chaotic properties of the interacting-boson model: A discovery of a new regular region

Alhassid, Y.; Whelan, Niall D.

doi:10.1103/physrevlett.67.816

Cited by 101 publications

(125 citation statements)

References 17 publications

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“…The study of chaotic properties of the Interacting Boson Approximation (IBA) model [1], both classically and quantum mechanically, led to the discovery [2,3] of a narrow strip of nearly regular behavior inside the symmetry triangle [4] of the IBA, connecting the U(5) and SU (3) limiting symmetries, in addition to the regular region along the U(5)-O(6) leg of the triangle.…”

Section: Introductionmentioning

confidence: 99%

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

2011

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Using the contraction of the SU(3) algebra to the algebra of the rigid rotator in the large boson number limit of the Interacting Boson Approximation (IBA) model, a line is found inside the symmetry triangle of the IBA, along which the SU(3) symmetry is preserved. 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, and lies within the AlhassidWhelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices amidst chaotic regions. In addition to providing an explanation for the existence of the arc of regularity, the present line represents the first example of an analytically determined approximate symmetry in the interior of the symmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenable to contraction. This condition is equivalent to algebras in which the equilibrium ground state (and its rotational band) become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA for large numbers of valence nucleons.

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Section: Introductionmentioning

confidence: 99%

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

2011

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“…5 corresponds to a deformed nucleus lying along the arc of regularity (red dot). The arc is a unique region, discovered by Alhassid and Whelan [9] about twenty years ago where, amidst nuclei whose properties appear to be highly chaotic, there is a narrow valley of regularity starting at SU(3) and heading towards the spherical-deformed phase transitional line and then beyond towards U(5). In this valley, despite the distance from SU(3), the spectra regain ordered behavior.…”

Section: Results For Nuclei Deviating From the Dynamical Symmetriesmentioning

confidence: 99%

“…We start with the dynamical symmetries O(6) and SU (3) [all E0 transitions are identically zero in U(5)] and then look at cases in the interior of the symmetry triangle of the IBA, including a calculation along the arc of regularity [9]. We will do the calculations for different numbers of valence nucleons to check for consistency of the results.…”

Section: Introductionmentioning

confidence: 99%

E0transitions in deformed nuclei

Ilie

Casten

2011

Phys. Rev. C

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E0 transitions are a sensitive indicator of structure in nuclei, reflecting shape transitional regions, deformation and intruder states. Attention has generally focused on E0 transitions to the ground state or low lying yrast levels. In this paper we look at all E0 transitions connecting 0 + states in a rather general collective model. We deduce a new selection rule and map out calculated strengths throughout the spectrum. The distributions of E0 strengths for several different collective structures are discussed.

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“…It has been found that chaotic behavior prevails over most of the symmetry triangle, with the noticeable exception of two regions, in which highly regular behavior is observed [12]. One of them is located along the U(5)-O(6) line, and its existence is due to the O(5) symmetry known to survive along the whole line [13].…”

mentioning

confidence: 99%

“…One of them is located along the U(5)-O(6) line, and its existence is due to the O(5) symmetry known to survive along the whole line [13]. The other regular region is connecting U(5) and SU(3) through a narrow path within the triangle, called the Alhassid-Whelan arc of regularity [12] (also shown in Fig. 1), the symmetry implying its existence being yet unknown.…”

mentioning

confidence: 99%

0[sup +] states in the large boson number limit of the Interacting Boson Approximation model

Bonatsos¹,

McCutchan²,

Casten³

2008

AIP Conference Proceedings

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Abstract.Studies of the Interacting Boson Approximation (IBA) model for large boson numbers have been triggered by the discovery of shape/phase transitions between different limiting symmetries of the model. These transitions become sharper in the large boson number limit, revealing previously unnoticed regularities, which also survive to a large extent for finite boson numbers, corresponding to valence nucleon pairs in collective nuclei. It is shown that energies of 0 + n states grow linearly with their ordinal number n in all three limiting symmetries of IBA [U(5), SU(3), and O(6)]. Furthermore, it is 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, while the energy ratio E(6 + 1 )/E(0 + 2 ) turns out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first-and second-order transitions. The energies of 0 + n states near the point of the first order shape/phase transition between U(5) and SU(3) are shown to grow as n(n+3), in agreement with the rule dictated by the relevant critical point symmetries resulting in the framework of special solutions of the Bohr Hamiltonian. The underlying partial dynamical symmetries and quasi-dynamical symmetries are also discussed. The Interacting Boson Approximation (IBA) model [1], describing collective phenomena in atomic nuclei in terms of s and d bosons (of angular momentum 0 and 2, respectively), is known to possess an overall U(6) symmetry, containing three different dynamical symmetries, U(5), SU(3), and O(6), corresponding to near-spherical (vibrational), axially symmetric prolate deformed (rotational), and soft with respect to axial asymmetry (γ-unstable) nuclei respectively. These limiting symmetries are shown at the vertices of the symmetry triangle [2] of the model, shown in Fig. 1. KeywordsAn energy functional can be obtained [4] in the classical limit of the model, through the use of the coherent state formalism [5,6]. Studying this energy functional in the framework of catastrophe theory one can see [7] that a first order phase transition (in the Ehrenfest classification) is predicted to occur between the limiting symmetries U(5) and SU(3), while a second order phase transition is expected between U(5) and O(6). We refer to these transitions as shape/phase transitions. A narrow shape coexistence region is then predicted [4] in the symmetry triangle of the IBA, separating the spherical and deformed phases. The shape coexistence region shrinks into the point of second order phase transition as the U(5)-O(6) line is approached, as shown in Fig. 1.

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Chaotic properties of the interacting-boson model: A discovery of a new regular region

Cited by 101 publications

References 17 publications

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

E0transitions in deformed nuclei

0[sup +] states in the large boson number limit of the Interacting Boson Approximation model

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