Effects of pairing in the pseudo-SU(3) model

Troltenier, D.; Bahri, C.; Draayer, J. P.

doi:10.1016/0375-9474(95)00078-f

Cited by 22 publications

(12 citation statements)

References 39 publications

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“…Turning briefly to the situation with κ πν = −1, for the N π = 6 and N ν = 8 system, the (λ, µ) are (48,36), (47,35), (46,34) (48,36)L, (47,35) and (46,34).…”

Section: E B(e2) and B(m 1) Results From Sdgiibm-2mentioning

confidence: 99%

“…2). These degeneracies will be lifted and the band structures maintained by adding to H Q the SU(3) ⊃ SO(3) integrity basis operators [11,43,46,47].…”

Section: B M 1 and E2 Matrix Elementsmentioning

confidence: 99%

“…Considering κ πν = −1, for the N π = 8 and N ν = 12 system, the (λ, µ) are (48,32), (47,31), (46,30) and so on; see Eq. ( 17).…”

Section: Starting With Hmentioning

confidence: 99%

“…. B(E2) and B(M 1) results from sdgIBM-2: κ πν = −1Considering κ πν = −1, for the N π = 8 and N ν = 12 system, the (λ, µ) are(48,32),(47,31),(46,30) and so on; see Eq.(17). These will give for example the K bands,(48,32) K=0,2,4,... , (47, 31) K=1,3,5,... , (46, 30) K=0,2,4,... .…”

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confidence: 99%

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Multiple SU(3) Algebras in Interacting Boson Model and Shell Model

Kota

2020

SU(3) Symmetry in Atomic Nuclei

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Rotational SU (3) algebraic symmetry continues to generate new results in the shell model (SM). Interestingly, it is possible to have multiple SU (3) algebras for nucleons occupying an oscillator shell η. Several different aspects of the multiple SU (3) algebras are investigated using shell model and also deformed shell model based on Hartree-Fock single particle states with nucleons in sdg orbits giving four SU (3) algebras. Results show that one of the SU (3) algebra generates prolate shapes, one oblate shape and the other two also generate prolate shape but one of them gives quiet small quadrupole moments for low-lying levels. These are inferred by using the standard form for the electric quadrupole transition operator and using quadrupole moments and B(E2) values in the ground K = 0 + band in three different examples. Multiple SU (3) algebras extend to interacting boson model and using sdgIBM, the structure of the four SU (3) algebras in this model are studied by coherent state analysis and asymptotic formulas for E2 matrix elements.The results from sdgIBM further support the conclusions from the sdg shell model examples.

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“…Turning briefly to the situation with κ πν = −1, for the N π = 6 and N ν = 8 system, the (λ, µ) are (48,36), (47,35), (46,34) (48,36)L, (47,35) and (46,34).…”

Section: E B(e2) and B(m 1) Results From Sdgiibm-2mentioning

confidence: 99%

“…2). These degeneracies will be lifted and the band structures maintained by adding to H Q the SU(3) ⊃ SO(3) integrity basis operators [11,43,46,47].…”

Section: B M 1 and E2 Matrix Elementsmentioning

confidence: 99%

“…Considering κ πν = −1, for the N π = 8 and N ν = 12 system, the (λ, µ) are (48,32), (47,31), (46,30) and so on; see Eq. ( 17).…”

Section: Starting With Hmentioning

confidence: 99%

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confidence: 99%

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Multiple SU(3) Algebras in Interacting Boson Model and Shell Model

Kota

2020

SU(3) Symmetry in Atomic Nuclei

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“…In 1994, Bahri and Draayer completed an improved code for faster calculations [12]. Later the effects of paring interaction on the K-band mixing were studied [13,14] by Trotelnier, Bahri, Escher and Draayer within the framework of the pseudo-SU(3) model.…”

Section: Introductionmentioning

confidence: 99%

Description of heavy deformed nuclei within the pseudo-SU(3) shell model

Popa

Georgieva

2012

J. Phys.: Conf. Ser.

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Abstract. We present a review of the pseudo-SU(3) shell model and its application to heavy deformed nuclei. The model have been applied to describe the low energy spectra, B(E2) and B(M1) values. A systematic study of each part of the interaction within the Hamiltonian was carried out. The study leads us to a consistent method of choosing the parameters in the model. A systematic application of the model for a sequence of rare earth nuclei demonstrates that an overarching symmetry can be used to predict the onset of deformation as manifested through low-lying collective bands.The scheme utilizes an overarching sp(4,R) algebraic framework. IntroductionOver the past years many calculations were carried out by using the SU(3) shell model and the pseudo-SU(3) symmetry. Ongoing improvements and innovations in experimental techniques (4π detectors, radioactive beams, etc.) anticipate the identification of additional new phenomena in the near future, and more information about the existing ones. However, it is commonly accepted that the nuclear shell model should be able to address most of these issues and provide answers. The problem is that most shell-model theories are limited by the large dimensions of the required model spaces, which increases unmanageably with the number of nucleons A. Furthermore, more microscopic calculations are needed exactly in the region of heavy nuclei, in the mass range A ≥ 100.Having this problem, it is essential to take full advantage of symmetries, those that are exact, as well as those which are only partially fulfilled.The selection rules that are associated with such symmetries generate, respectively, weakly coupled and disconnected subspaces of the full space and this allows for a significant reduction in the dimensionality of the model space. The symmetry used here is the pseudo-spin symmetry.A shell model theory for heavy nuclei requires a severe truncation of the model space. To reproduce the essential physics found in the low-energy states of a large space in a smaller one, we have to select the basis states relative to those parts of the interaction that dominate the low-energy structure. Nuclear physics supports the view that the nuclear effective interaction appropriate to low-energy excitations must have a strong correlation with the pairing and quadrupole-quadrupole interactions. The Q · Q interaction, which dominates for near midshell nuclei, is known to introduce deformation and led to the introduction of the SU(3) shell model. This led also to a very natural way to truncate large model spaces, namely to consider few basis states in correspondence with the eigenvalue of Q · Q operator.

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$$SU(3) \supset SO(3)$$ Integrity Basis Operators

Kota

2020

SU(3) Symmetry in Atomic Nuclei

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Effects of pairing in the pseudo-SU(3) model

Cited by 22 publications

References 39 publications

Multiple SU(3) Algebras in Interacting Boson Model and Shell Model

Multiple SU(3) Algebras in Interacting Boson Model and Shell Model

Description of heavy deformed nuclei within the pseudo-SU(3) shell model

$$SU(3) \supset SO(3)$$ Integrity Basis Operators

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