Relationship between the Bohr-Mottelson model and the interacting boson model

Klein, Abraham; Li, Ching-Teh; Vallières, M.

doi:10.1103/physrevc.25.2733

Cited by 18 publications

(7 citation statements)

References 33 publications

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“…N → ∞) limit of hamiltonian (2). The classical hamiltonian (6) can be equivalently obtained using condensate states [8,9,43,44,[118][119][120][121][122][123]…”

Section: Quantum Phase Transitions In Finite Bosonic Systemsmentioning

confidence: 99%

“…For instance, in the latter model the ground state of a spherical nucleus is treated as the vacuum, a state with N = 0, while in the IBM the same state coincides with a condensate of s bosons with given N > 0. In spite of these differences, both models can be connected and rooted in an underlying microscopic treatment [123,[152][153][154].…”

Section: Foundations and The Algebraic Structurementioning

confidence: 99%

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Quantum phase transitions in the interacting boson model

Cejnar¹,

Jolie

2009

Progress in Particle and Nuclear Physics

189

111

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This review is focused on various properties of quantum phase transitions (QPTs) in the Interacting Boson Model (IBM) of nuclear structure. The model in its infinite-size limit exhibits shape-phase transitions between spherical, deformed prolate, and deformed oblate forms of the ground state. Finite-size precursors of such behavior are verified by robust variations of nuclear properties (nuclear masses, excitation energies, transition probabilities for low lying levels) across the chart of nuclides. Simultaneously, the model serves as a theoretical laboratory for studying diverse general features of QPTs in interacting many-body systems, which differ in many respects from lattice models of solid-state physics. We outline the most important fields of the present interest: (a) The coexistence of first- and second-order phase transitions supports studies related to the microscopic origin of the QPT phenomena. (b) The competing quantum phases are characterized by specific dynamical symmetries and novel symmetry related approaches are developed to describe also the transitional dynamical domains. (c) In some parameter regions, the QPT-like behavior can be ascribed also to individual excited states, which is linked to the thermodynamic and classical descriptions of the system. (d) The model and its phase structure can be extended in many directions: by separating proton and neutron excitations, considering odd-fermion degrees of freedom or different particle-hole configurations, by including other types of bosons, higher order interactions, and by imposing external rotation. All these aspects of IBM phase transitions are relevant in the interpretation of experimental data and important for a fundamental understanding of the QPT phenomenon.Comment: a review article, 71 pages, 18 figure

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“…N → ∞) limit of hamiltonian (2). The classical hamiltonian (6) can be equivalently obtained using condensate states [8,9,43,44,[118][119][120][121][122][123]…”

Section: Quantum Phase Transitions In Finite Bosonic Systemsmentioning

confidence: 99%

Section: Foundations and The Algebraic Structurementioning

confidence: 99%

Quantum phase transitions in the interacting boson model

Cejnar¹,

Jolie

2009

Progress in Particle and Nuclear Physics

189

111

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“…Setting p =0 defines a potential-energy surface whose p geometrical structure determines the "shape" of the system Klein, Li, and Vallieres, 1982b). …”

Section: B Relation Of Interacting Boson Modelmentioning

confidence: 99%

Boson realizations of Lie algebras with applications to nuclear physics

1991

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The concept of boson realization (or mapping) of Lie algebras appeared first in nuclear physics in 1962 as the idea of expanding bilinear forms in fermion creation and annihilation operators in Taylor series of boson operators, with the object of converting the study of nuclear vibrational motion into a problem of coupled oscillators. The physical situations of interest are quite diverse, depending, for instance, on whether excitations for fixed-or variable-particle number are being studied, on how total angular momentum is decomposed into orbital and spin parts, and on whether isotopic spin and other intrinsic degrees of freedorn enter. As a consequence, all of the semisimple algebras other than the exceptional ones have proved to be of interest at one time or another, and all are studied in this review. Though the salient historical facts are presented in the introduction, in the body of the review the progression is (generally) from the simplest algebras to the more complex ones. With a sufficiently broad view of the physics requirements, the mathematical problem is the realization of an arbitrary representation of a Lie algebra in a subspace of a suitably chosen Hilbert space of bosons (Heisenberg-Weyl algebra). Indeed, if one includes the study of odd nuclei, one is forced to consider the mappings to spaces that are direct-product spaces of bosons and (quasi)fermions. Though all the methods that have been used for these problems are reviewed, emphasis is placed on a relatively new algebraic method that has emerged over the past decade. Many of the classic results are rederived, and some new results are obtained for odd systems. The major application of these ideas is to the derivation, starting from the shell model, of the phenomenological models of nuclear collective motion, in particular, the geometric model of Bohr and Mottelson and the more recently developed interacting boson model of Arirna and Iachello. A critical discussion of those applications is interwoven with the theoretical developments on which they are based; many other applications are included, some of practical interest, some simply to illustrate the concepts, and some to suggest new lines of inquiry.

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“…where q u andp u are the coordinates and the associated momenta in spherical tensor form [16,17] withÃ u = (−) u A −u , and using the definition of Casimir operator of the Eu(5) group, C 2,Eu(5) =p 2 (see, for example, Ref. [13]), one can give the algebraic Hamiltonian with the Eu(5) DS,…”

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confidence: 99%

Euclidean dynamical symmetry in nuclear shape phase transitions

et al. 2014

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The Euclidean dynamical symmetry hidden in the critical region of nuclear shape phase transitions is revealed by a novel algebraic F(5) description. With a nonlinear projection, it is shown that the dynamics in the critical region of the spherical-axial deformed and the spherical-γ soft shape phase transitions can indeed be manifested by this description, which thus provides a unified symmetry-based interpretation of the critical phenomena in the region. PACS numbers: 21.60.Fw, 21.60.Ev, 21.10.Re, 64.70.Tg Dynamical symmetries (DSs) play an important role in elucidating the quintessential nature of quantum many-body dynamical structures, especially their evolution under changing conditions. Typical examples of DS are those associated with the interacting boson model (IBM) [1] for nuclear structure and the vibron model (VM) [2] for molecules and atomic clusters [3], where various DSs provide considerable insight into the nature of shape phases and shape phase transitions (SPTs) [4].

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Relationship between the Bohr-Mottelson model and the interacting boson model

Cited by 18 publications

References 33 publications

Quantum phase transitions in the interacting boson model

Quantum phase transitions in the interacting boson model

Boson realizations of Lie algebras with applications to nuclear physics

Euclidean dynamical symmetry in nuclear shape phase transitions

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