Configuration mixing in the<i>sdg</i>interacting boson model

Bouldjedri, A.; Isacker, P. Van; Zerguine, S.

doi:10.1088/0954-3899/31/11/014

Cited by 4 publications

(5 citation statements)

References 40 publications

(71 reference statements)

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“…, , is used as the label of orthogonal algebra generated by the three levels a, b and c. Figure 2 shows also the lattice of algebras in the U 21…”

Section: The Dynamical Symmetriesmentioning

confidence: 99%

“…The SGA of the IBM is the unitary algebra U 6 . One obvious extension is gIBM [16][17][18][19][20][21] in which the next even angular momentum is considered hence to include a g−(l=4) boson. The U 15 is the SGA of the gIBM.…”

Section: Introductionmentioning

confidence: 99%

“…Interestingly, some of our considered DSs and energy formulae have particular realizations in IBM. Kota et al [16][17][18][19][20][21], categorized the DSs of sdgIBM into seven types. Some of them are unraveled in our general three DSs.…”

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confidence: 99%

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Some algebraic structures for the bosonic three-level systems

et al. 2018

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A simple systematic procedure to construct the three-level unitary and orthogonal algebras which appear in the bosonic three -level pairing models and for arbitrary choice of level degeneracies is presented. We draw attention to the existence of the three types of dynamical symmetry. The new analytical expressions of the energies are derived. The results presented show very clearly the duality between orthogonal algebras and the quasi-spin algebras for the three-level system with pairing interactions. The seniority selection rules of the transition operators in three level boson system are given. Illustrative calculations are carried out for U 21 algebra.

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“…, , is used as the label of orthogonal algebra generated by the three levels a, b and c. Figure 2 shows also the lattice of algebras in the U 21…”

Section: The Dynamical Symmetriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Some algebraic structures for the bosonic three-level systems

et al. 2018

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“…To do otherwise would require a hexadecapole operator taken from one of the other two strong coupling limits of sdg-IBM, SU(5) or SU (6). Since these have a questionable microscopic interpretation [52], this is not done here.…”

Section: A Generalized Casten Trianglementioning

confidence: 99%

Phase transitions in the sdg interacting boson model

2010

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Abstract. A geometric analysis of the sdg interacting boson model is performed. A coherent-state is used in terms of three types of deformation: axial quadrupole (β 2 ), axial hexadecapole (β 4 ) and triaxial (γ 2 ). The phase-transitional structure is established for a schematic sdg hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical U(5) ⊗ U(9), the (prolate and oblate) deformed SU ± (3) and the γ 2 -soft SO(15) limits. For realistic choices of the hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the sd version of the model and, in particular, no transition towards a stable triaxial shape is found.

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“…A minimum with octahedral shape requires mixing of s and g bosons, so as to induce hexadecapole deformation, and no or weak mixing of these with the d boson to ensure zero quadrupole deformation. These conditions rule out all limits where s, d and g bosons are strongly mixed on an equal footing, that is, they discard the SU(3), SU(6), SU (5) and SO(15) limits [18]. A strict decoupling of the s and g from the d bosons is obtained by the reduction…”

Section: Introductionmentioning

confidence: 99%

Higher-rank discrete symmetries in the IBM. II Octahedral shapes: Dynamical symmetries

Bouldjedri

Zerguine

Isacker

2020

Preprint

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The symmetries of the sdg-IBM, the interacting boson model with s, d and g bosons, are studied as regards the occurrence of shapes with octahedral symmetry. It is shown that no sdg-IBM Hamiltonian with a dynamical symmetry displays in its classical limit an isolated minimum with octahedral shape. However, a degenerate minimum that includes a shape with octahedral symmetry can be obtained from a Hamiltonian that is transitional between two limits, U g (9) ⊗ U d (5) and SO sg (10) ⊗ U d (5), and the conditions for its existence are derived. An isolated minimum with octahedral shape, either an octahedron or a cube, may arise through a modification of two-body interactions between the g bosons. Comments on the observational consequences of this construction are made.

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Configuration mixing in thesdginteracting boson model

Cited by 4 publications

References 40 publications

Some algebraic structures for the bosonic three-level systems

Some algebraic structures for the bosonic three-level systems

Phase transitions in the sdg interacting boson model

Higher-rank discrete symmetries in the IBM. II Octahedral shapes: Dynamical symmetries

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