Relationship between the Bohr Collective Hamiltonian and the Interacting-Boson Model

Ginocchio, Joseph N.; Kirson, Michael W.

doi:10.1103/physrevlett.44.1744

Cited by 406 publications

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“…This yields a function of the deformation variables which can be interpreted as a total energy surface depending on these variables. The method was first proposed for the sd-IBM [33,34]. The extension to the sdg-IBM was carried out by Devi and Kota [35] for the simplified parameterization (3).…”

Section: Classical Limit Of the Sdg-ibmmentioning

confidence: 99%

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

2015

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Section: Classical Limit Of the Sdg-ibmmentioning

confidence: 99%

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

2015

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“…In the context of an algebraic approach to nuclear structure, the concept of phase transitions was developed a number of years ago using the intrinsic state formalism [13,22,23] More recently, critical point transitions have been described in a geometrical framework, in terms of the Bohr Hamiltonian. These new CPS, E(5) [3] and X(5) [4], correspond to second and first order phase transitions between a vibrator and a rotor, differing in the γ degree of freedom.…”

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“…Further, we will show that a particular value of this observable identifies the entire critical region, even for structures not satisfying a specific CPS. Finally we use this value to point to the possible existence of a heretofore undefined new symmetry at the critical point.In the context of an algebraic approach to nuclear structure, the concept of phase transitions was developed a number of years ago using the intrinsic state formalism [13,22,23] …”

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Simple Empirical Order Parameter for a First-Order Quantum Phase Transition in Atomic Nuclei

et al. 2008

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A simple, empirical signature of a first order phase transition in atomic nuclei is presented, the ratio of the energy of the 6 + level of the ground state band to the energy of the first excited 0 + state. This ratio provides an effective order parameter which is not only easy to measure, but also distinguishes between first and second order phase transitions and takes on a special value in the critical region. Data in the Nd-Dy region show these characteristics. In addition, a repeating degeneracy between alternate yrast states and successive excited 0 + states is found to correspond closely to the line of a first order phase transition in the framework of the Interacting Boson Approximation (IBA) model in the large N limit, pointing to a possible underlying symmetry in the critical region.The study of structural evolution in atomic nuclei has witnessed significant developments in recent years. One of the most important has been the discovery of empirical evidence [1,2] for quantum phase transitions (QPT) in the equilibrium shape as a function of nucleon number. This has led to the proposal [3,4] and empirical verification [5,6] of a new class of models, called critical point symmetries (CPS). These, in turn have spurred an abundance of experimental searches [7,8,9] for nuclei satisfying the predictions of these CPS as well as investigations into the presence of quasidynamical and partial dynamical symmetries at the critical point [10,11].In contrast to the usual thermodynamic phase transitions [12], QPT occur at zero temperature as a parameter in the Hamiltonian is varied [13]. They are attracting much attention in a variety of physical systems, including Josephson-junction arrays and quantum Hall-effect systems [14]. The transition from BardeenCooper-Schrieffer (BCS) pairing correlations [15] to Bose-Einstein condensation (BEC) as a result of increasing the strength of the pairing interaction in ultracold alkali atoms has been recently seen experimentally [16,17,18]. In nonrigid polyatomic molecules, a transition from rigidly-linear to rigidly-bent shapes has also been studied [19]. A relationship between QPT and quantum entanglement has also attracted much attention [20,21]. Central to this active field is the search for simple empirical signatures of QPT and the identification of their order. The properties of QPT in atomic nuclei are therefore of quite broad interest, especially since nuclei are finite-body systems in which the number of constituents can be varied experimentally and theoretically.It is the purpose of this Letter to identify a new, easyto-measure, observable in one such system, atomic nuclei, that acts as an order parameter for QPT in nuclei and which can distinguish first and second order phase transitions. Further, we will show that a particular value of this observable identifies the entire critical region, even for structures not satisfying a specific CPS. Finally we use this value to point to the possible existence of a heretofore undefined new symmetry at the critical point.In the co...

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“…An 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).…”

Section: Introductionmentioning

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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Relationship between the Bohr Collective Hamiltonian and the Interacting-Boson Model

Cited by 406 publications

References 1 publication

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian

Simple Empirical Order Parameter for a First-Order Quantum Phase Transition in Atomic Nuclei

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

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