A coupled rotor-vibrator model as the macroscopic limit of the microscopic symplectic model

Blanc, R. Le; Carvalho, J.; Rowe, D.J.

doi:10.1016/0370-2693(84)90910-9

Cited by 45 publications

(19 citation statements)

References 11 publications

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“…The proof takes advantage of the well known contraction [18] of the SU(3) algebra to the [R 5 ]SO(3) algebra [19,20] of the rigid rotator [21]. Furthermore, using the contraction of O(6) to the [R 5 ]SO(5) algebra [22,23] of the γ-unstable rotator, we prove that no line related to the O(6) symmetry exists within the triangle.…”

Section: Introductionmentioning

confidence: 87%

“…(19) has been derived in the special case of considering matrix elements within the ground state band only. This is similar to the condition discussed earlier in the context of Eq.…”

Section: Matrix Elementsmentioning

confidence: 99%

“…[9]) and E(4 14), and as predicted by the findings of the present work, Eqs. (13) and (19). The η axis has been reversed, in order to correspond directly to Fig.…”

Section: Appendix 3 Matrix Elementsmentioning

confidence: 99%

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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: 87%

“…(19) has been derived in the special case of considering matrix elements within the ground state band only. This is similar to the condition discussed earlier in the context of Eq.…”

Section: Matrix Elementsmentioning

confidence: 99%

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

2011

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“…7. Moreover, it has been shown [18,19,20] that, in the limit of large quantum numbers, the Sp(3, R) model contracts to the coupled product of a Bohr vibrational model and a rotor model. This is the so-called coupled rotor-vibrator limit of the symplectic model.…”

Section: Irreducible Representations (Irreps) Of Sp(3 R) In a U(3) Bmentioning

confidence: 99%

The fundamental role of symmetry in nuclear models

Rowe

2013

AIP Conference Proceedings

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Abstract. The purpose of these lectures is to illustrate how symmetry and pattern recognition play essential roles in the progression from experimental observation to an understanding of nuclear phenomena in terms of interacting neutrons and protons. We do not discuss weak interactions nor relativistic and sub-nucleon degrees of freedom. The explicit use of symmetry and the power of algebraic methods, in combination with analytical and geometrical methods are illustrated by their use in deriving a shell-model description of nuclear rotational dynamics and the structure of deformed nuclei.

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“…These should be chosen so as to minimize H~ ~ In other words, the interaction between the collective and non-collective subspaces (20) and (21) should be made to vanish (in some approximation) by the choice of the IBM bosons. To this end, we introduce a unitary transformation U [13] which ensures that, up to a certain order, the transformed hamiltonian ~= UH B U + (26) leaves invariant the collective subspacc (20). In this case, the operators…”

Section: N~oul=x Y; Z Wd54([b? • B~y ~ [~3 • ~4y~)mentioning

confidence: 99%

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Kuchta¹

1988

Z. Physik A - Atomic Nuclei

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Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to light sd-shell nuclei. The key ingredients of our approach are: a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure; b) two successive unitary transformations that extract the "maximally (s~, s~) and J decoupled" collective bosons with angular momenta J=0 + s~+, + + + d+~(T= 0), d+~(T= 1)).The method is applied to obtain the low-energy spec-= 2(d,~,,, d~, tra and the electron scattering form factors for the 0~-~2~-transitions in g~ and 24Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s~+~, d~+~ (T= 1), d~+~(T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.

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A coupled rotor-vibrator model as the macroscopic limit of the microscopic symplectic model

Cited by 45 publications

References 11 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

The fundamental role of symmetry in nuclear models

Microscopic foundation of the interacting boson model in thes d-shell nuclei

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