Systematics in the structure of low-lying, nonyrast bandhead configurations of strongly deformed nuclei

Popa, Gabriela; Georgieva, A. I.; Draayer, J. P.

doi:10.1103/physrevc.69.064307

Cited by 10 publications

(19 citation statements)

References 26 publications

(33 reference statements)

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“…For nuclei from Table 3, in the middle of the shell, the ground and the γ band belong to the same (λ, µ) with λ > µ. At the limits of the deformed region the ground band states have oblate deformation (λ < µ) and the K π = 0 + 2 and the K π = 2 + 1 bands are mixed in the same SU(3) irrep [18]. The analysis for nuclei from Table 4 is under investigation.…”

Section: Results and Conclusionmentioning

confidence: 97%

“…The resulted fitted parameters of the rotor part of the Hamiltonian are given in the fourth to seventh columns. [18,20]. The main reason for obtaining the position of each collective band with respect to each other, as well as of each level within the band is the specific content of the obtained SU(3) irreps into the collective states, which is related to their deformations.…”

Section: Results and Conclusionmentioning

confidence: 99%

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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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Section: Results and Conclusionmentioning

confidence: 97%

Section: Results and Conclusionmentioning

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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“…The Hamiltonian with the considered dynamical symmetry (25) is expressed in terms of the first and second order Casimir operators of the different subgroups in its corresponding chain (16):…”

Section: Reduction Through the Non-compact Sp(2r) 221 Algebraic Cmentioning

confidence: 99%

“…The variety of possible choices for the correspondence of the excited bands to sequences of states in the symplectic space and the mixing of the rotational and vibrational degrees of freedom like in the U (6)-limit allows us to reproduce correctly the behavior of the excited bands with respect to one another, which can change a lot even in neighboring nuclei [25].…”

Section: Application To Real Nucleimentioning

confidence: 99%

Unified dynamical symmetries in the symplectic extension of the interacting vector boson model

Georgieva

Ganev

Draayer

et al. 2008

J. Phys.: Conf. Ser.

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The algebraic Interacting Vector Boson Model (IVBM) is extended by exploiting three new subgroup chains in the reduction of its highest symplectic dynamical symmetry group Sp(12,R) to the physical angular momentum subgroup SO(3). The corresponding exactly solvable limiting cases are applied to achieve a description of complex nuclear collective spectra of even-even nuclei in the rare earth and actinide regions up to states of very high angular momentum.First we exploit two reductions in which collective modes can be mixed, and obtain successful descriptions of both positive and negative parity band configurations. The structure of bandhead configurations, whose importance is established in the first two limits, is examined in a third reduction, that also provides important links between the subgroups of the other limits.

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“…For example, the states of first excited β−band and/or γ-band may belong to two different diagonals (λ, µ = 0), K = 0 and/or to (λ, µ = 2), K = 0 and/or 2, so that ν = L or/and ν = L − 2 for L-even and ν = L − 1 for Lodd respectively and ∆ν = 2 for each neighboring su(3) multiplets in a band under consideration. This variety of possible choices for the excited bands allows us to reproduce correctly the behavior of these bands with respect to one another, which can change a lot even in neighboring nuclei because of the mixing of the vibrational and rotational collective modes [28].…”

Section: Application To Real Nucleimentioning

confidence: 99%

Six-dimensional Davidson potential as a dynamical symmetry of the symplectic interacting vector boson model

2005

Self Cite

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A six-dimensional Davidson potential, introduced within the framework of the Interacting Vector Boson Model (IVBM), is used to describe nuclei that exhibit transitional spectra between the purely rotational and vibrational limits of the theory. The results are shown to relate to a new dynamical symmetry that starts with the Sp(12, R) ⊃ SU (1, 1) × SO(6) reduction. Exact solutions for the eigenstates of the model Hamiltonian in the basis defined by a convenient subgroup chain of SO (6) are obtained. A comparison of the theoretical results with experimental data for heavy nuclei with transitional spectra illustrates the applicability of the theory.

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Systematics in the structure of low-lying, nonyrast bandhead configurations of strongly deformed nuclei

Cited by 10 publications

References 26 publications

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

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

Unified dynamical symmetries in the symplectic extension of the interacting vector boson model

Six-dimensional Davidson potential as a dynamical symmetry of the symplectic interacting vector boson model

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