The coupled-rotor-vibrator model

Rowe, D.J.; Vassanji, M.G.; Carvalho, J.

doi:10.1016/0375-9474(89)90283-2

Cited by 46 publications

(42 citation statements)

References 52 publications

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“…In the limit of large values of C 2 (λ, µ) and λ ≥ µ the intrinsic quadrupole moments become [20,46] …”

Section: Appendix 1 Commutation Relationsmentioning

confidence: 99%

“…As a result, in the SU(3) framework one is interested in states with large values of C 2 (λ, µ) and λ < µ, in which the intrinsic quadrupole moments become [20,46] …”

Section: Appendix 1 Commutation Relationsmentioning

confidence: 99%

“…Byχ we denote the Vergados quantum number [27] [not to be confused with the parameter χ of the Hamiltonian (1) This expression can be simplified since in the contraction limit the matrix elements of the quadrupole operator become [46] [N], (…”

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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“…In the limit of large values of C 2 (λ, µ) and λ ≥ µ the intrinsic quadrupole moments become [20,46] …”

Section: Appendix 1 Commutation Relationsmentioning

confidence: 99%

“…As a result, in the SU(3) framework one is interested in states with large values of C 2 (λ, µ) and λ < µ, in which the intrinsic quadrupole moments become [20,46] …”

Section: Appendix 1 Commutation Relationsmentioning

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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“…A different class of coherent state representation to those of the holomorphic kind was introduced in 1989 [19,20]. Its purpose was to construct the irreps of su(3) in an SO(3)-coupled basis, which is the basis appropriate for application to rotationally-invariant systems such as nuclei.…”

Section: Vcs Irreps Of Su(3) In An So(3) Basismentioning

confidence: 99%

Vector coherent state representations and their inner products

Rowe¹

2012

J. Phys. A: Math. Theor.

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Abstract. Several advances have extended the power and versatility of coherent state theory to the extent that it has become a vital tool in the representation theory of Lie groups and their Lie algebras. Representative applications are reviewed and some new developments are introduced. The examples given are chosen to illustrate special features of the scalar and vector coherent state constructions and how they work in practical situations. Comparisons are made with Mackey's theory of induced representations. For simplicity, we focus on square integrable (discrete series) unitary representations although many of the techniques apply more generally, with minor adjustment.

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“…A systematic way to derive matrix elements for a generic SU(3) irrep was given [2,3] in terms of vector coherent state [4,5] theory. VCS methods were also used in a derivation of SU(3) Clebsch-Gordan coefficients in an SO(3)-coupled basis [6,7].…”

Section: Su(3) Irreps and Their Asymptotic Limitsmentioning

confidence: 99%