The symplectic shell-model theory of collective states

Carvalho, J.; Blanc, R. Le; Vassanji, M.G.; Rowe, D.J.; McGrory, J.B.

doi:10.1016/0375-9474(86)90308-8

Cited by 57 publications

(25 citation statements)

References 26 publications

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“…In addition, similar SU(3) Hamiltonians to that given in (17) as well as more generalized forms were considered earlier by a number authors in the SU (3) shell model [35][36][37][38][39][40]. Our present investigation reveals such extension to the boson case is indeed feasible, which may provide additional insight into the SU(3) IBM theory from a more microscopic point of view [35].…”

Section: Discussionmentioning

confidence: 50%

“…(2) q are generators of the O(6) group; a Hamiltonian involving three-and four-body interactions in the SU(3) limit can generate a spectrum of the asymmetric rotor [34], which was based on previous description of the asymmetric rotor in the SU(3) shell model scheme [35][36][37][38][39][40]. As shown in these studies, the high-order interactions greatly enrich phase structures in the model even within the dynamical symmetry limit.…”

Section: Introductionmentioning

confidence: 99%

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Analytically solvable prolate-oblate shape phase transitional description within the SU(3) limit of the interacting boson model

et al. 2012

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A novel analytically solvable prolate-oblate shape phase transitional description for the SU (3) limit of the interacting boson model is investigated for finite-N as well as in the large-N classical limit. It is shown that the ground state shape phase transition is of first order due to level crossing.Through a comparison of the theoretical predictions with available experimental data for even-even 180 Hf, 182−186 W, [188][189][190][192][193][194][195][196][197][198] Pt, it is shown that this simple novel description is suitable for a description of the prolate-oblate shape phase transition in these nuclei.

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Section: Discussionmentioning

confidence: 50%

Section: Introductionmentioning

confidence: 99%

Analytically solvable prolate-oblate shape phase transitional description within the SU(3) limit of the interacting boson model

et al. 2012

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“…They play a role in diverse phenomena including nuclear and molecular spectroscopy [4][5][6][7][8][9][10][11][12][13][14][15][16], quantum phase transitions [17][18][19]24] and mixed regular and chaotic dynamics [20,21,25]. In this Letter, a hitherto unnoticed link is established between these two different symmetry concepts and it is shown that coherent mixing of one symmetry (QDS) can result in the partial conservation of a different, incompatible symmetry (PDS).…”

mentioning

confidence: 99%

“…This situation, referred to as partial dynamical symmetry (PDS) [4], was shown to be relevant to specific nuclei [4][5][6][7][8][9][10][11][12] and molecules [13]. In parallel, the notion of quasi dynamical symmetry (QDS) was introduced and discussed in the context of nuclear models [14][15][16][17][18][19][20][21]. While QDS can be defined mathematically in terms of embedded representations [22,23], its physical meaning is that several observables associated with particular eigenstates, may be consistent with a certain symmetry which in fact is broken in the Hamiltonian.…”

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confidence: 99%

Linking partial and quasi dynamical symmetries in rotational nuclei

et al. 2014

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“…In the context of the shell model, an SU(3) Hamiltonian of the type (2) has been considered by a number of authors [30][31][32][33][34][35]. Specifically, it was established [31] that the rotor Hamiltonian can be constructed from L 2 and the SU (3) invariants Ω and Λ.…”

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confidence: 99%

SU(3) realization of the rigid asymmetric rotor within the interacting boson model

2000

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It is shown that the spectrum of the asymmetric rotor can be realized quantum mechanically in terms of a system of interacting bosons. This is achieved in the SU(3) limit of the interacting boson model by considering higher-order interactions between the bosons. The spectrum corresponds to that of a rigid asymmetric rotor in the limit of infinite boson number.It is well known that the dynamical symmetry limits of the simplest version of the interacting boson model (IBM) [1,2], IBM-1, correspond to particular types of collective nuclear spectra. A Hamiltonian with U(5) dynamical symmetry [3] has the spectrum of an anharmonic vibrator, the SU(3) Hamiltonian [4] has the rotation-vibration spectrum of vibrations around an axially symmetric shape and the SO(6) Hamiltonian [5] yields the spectrum of a γ-unstable nucleus [6]. There exists another interesting type of spectrum frequently used to interpret nuclear collective excitations which corresponds to the rotation of a rigid asymmetric top [7] and which, up to now, has found no realization in the context of the IBM-1. The purpose of this letter is to extend the IBM-1 towards high-order terms such that a realization of the rigid non-axial rotor of Davydov and Filippov becomes possible. A pure group-theoretical approach is used that allows to establish the connection between algebraic and geometric Hamiltonians not only from the comparison of their spectra but also from the underlying group properties.Let us first recall some of the aspects that have enabled a geometric understanding of the IBM. The relation between the Bohr-Mottelson collective model [8] and the IBM has been established [9,10] on the basis of an intrinsic (or coherent) state for the IBM. Via this coherent-state formalism, a potential energy surface E(β, γ) in the quadrupole deformation variables β and γ can be derived for any IBM Hamiltonian and the equilibrium deformation parameters β 0 and γ 0 are then found by minimizing E(β, γ). It is by now well established that a one-and two-body IBM-1 Hamiltonian can give rise only to axially symmetric equilibrium shapes (γ 0 = 0 o or 60 o ) [9,10] and that a triaxial minimum in the potential energy surface requires at least three-body interactions [11].Since the relationship between γ-unstable model and rigid triaxial rotor was always an open question, Otsuka et al. [12,13] investigated in detail the SO(6) solutions of one-and two-body IBM-1 Hamiltonian. They found out that the triaxial intrinsic state with γ 0 = 30 o produces after the angular momentum projection the exact SO(6) eigenfunctions for small numbers of bosons N. Thus they conclude that for finite boson systems triaxiality reduces to γ-unstability.

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The symplectic shell-model theory of collective states

Cited by 57 publications

References 26 publications

Analytically solvable prolate-oblate shape phase transitional description within the SU(3) limit of the interacting boson model

Analytically solvable prolate-oblate shape phase transitional description within the SU(3) limit of the interacting boson model

Linking partial and quasi dynamical symmetries in rotational nuclei

SU(3) realization of the rigid asymmetric rotor within the interacting boson model

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