Algebraic benchmark for prolate-oblate coexistence in nuclei

Leviatan, A.; Shapira, Daniel

doi:10.1103/physrevc.93.051302

Cited by 30 publications

(31 citation statements)

References 53 publications

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“…The E2 decays between the spherical and deformed type of states are extremely weak, reflecting the impact of the high barrier. The ability of a single Hamiltonian to accommodate simultaneously states with different symmetry character, reinforces the view that partial symmetries can play a role in the phenomena of shape coexistence [7,11,12].…”

Section: Limitation Of the Standard Gcm Hamiltonian And A Possible Resupporting

confidence: 53%

Aspects of Shape Coexistence in the Geometric Collective Model of Nuclei

Georgoudis

Leviatan

2018

J. Phys.: Conf. Ser.

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We examine the coexistence of spherical and γ-unstable deformed nuclear shapes, described by an SO(5)-invariant Bohr Hamiltonian, along the critical-line. Calculations are performed in the Algebraic Collective Model by introducing two separate bases, optimized to accommodate simultaneously different forms of dynamics. We demonstrate the need to modify the β-dependence of the moments of inertia, in order to obtain an adequate description of such shape-coexistence. arXiv:1712.04392v1 [nucl-th]

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Section: Limitation Of the Standard Gcm Hamiltonian And A Possible Resupporting

confidence: 53%

Aspects of Shape Coexistence in the Geometric Collective Model of Nuclei

Georgoudis

Leviatan

2018

J. Phys.: Conf. Ser.

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“…The equilibrium deformations associated with the DS limits conform with their geometric interpretation and are given by β eq = 0 for U (5), (β eq = √ 2, γ eq = 0) for SU (3), (β eq = are manifested in nuclear structure, where extensive tests provide empirical evidence for their relevance to a broad range of nuclei [38,[40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. In addition to nuclear spectroscopy, Hamiltonians with PDS have been used in the study of quantum phase transitions [58,59,60] and of systems with mixed regular and chaotic dynamics [61,62]. In the present work, we show that this novel symmetry notion can play a vital role in formulating algebraic benchmarks for the dynamics of multiple quadrupole shapes.…”

Section: Dynamical Symmetries and Nuclear Shapesmentioning

confidence: 99%

Partial dynamical symmetries and shape coexistence in nuclei

Leviatan¹,

Gavrielov²

2017

Phys. Scr.

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Abstract. We present a symmetry-based approach for shape coexistence in nuclei, founded on the concept of partial dynamical symmetry (PDS). The latter corresponds to a situation when only selected states (or bands of states) of the coexisting configurations preserve the symmetry while other states are mixed. We construct explicitly critical-point Hamiltonians with two or three PDSs of the type U(5), SU(3), SU(3) and SO(6), appropriate to double or triple coexistence of spherical, prolate, oblate and γ-soft deformed shapes, respectively. In each case, we analyze the topology of the energy surface with multiple minima and corresponding normal modes. Characteristic features and symmetry attributes of the quantum spectra and wave functions are discussed. Analytic expressions for quadrupole moments and E2 rates involving the remaining solvable states are derived and isomeric states are identified by means of selection rules.Keywords: dynamical symmetry, partial dynamical symmetry, shape coexistence in nuclei, interacting boson model. IntroductionThe presence in the same nuclei, at similar low energies, of two or more sets of states which have distinct properties that can be interpreted in terms of different shapes, is a ubiquitous phenomena across the nuclear chart [1,2] [11,12], and the triple coexistence of spherical, prolate and oblate shapes in 186 Pb [13]. A detailed microscopic interpretation of nuclear shape-coexistence is a formidable task. In a shell model description of nuclei near shell-closure, it is attributed to the occurrence of multi-particle multi-hole intruder excitations across shell gaps. For medium-heavy nuclei, this necessitates drastic truncations of large model spaces, e.g., by Monte Carlo sampling [14,15] or by a bosonic approximation of nucleon pairs [16][17][18][19][20][21][22][23][24][25]. In a mean-field approach, based on energy density functionals, the coexisting shapes are associated with different minima of an energy surface calculated self-consistently. A detailed comparison with spectroscopic observables requires beyond mean-field methods, including restoration of broken symmetries and configuration mixing of angular-momentum and particle-number projected states [26,27]. Such extensions present a major computational effort and often require simplifying assumptions such as axial symmetry and/or a mapping to collective model Hamiltonians [23][24][25][26][27][28].A recent global mean-field calculation of nuclear shape isomers identified experimentally accessible regions of nuclei with multiple minima in their potential-energy surface [29,30]. Such

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“…Cubic terms of the type present inV 0 , Eq. (6), were previously encountered in IBM studies of triaxiality [42,43], signature splitting [39,44], band anharmonicity [40,45], and shape-coexistence [46,47] in deformed nuclei. Such higher-order terms show up naturally in microscopicinspired IBM Hamiltonians derived by a mapping from self-consistent mean-field calculations [48,49].…”

Section: 00mentioning

confidence: 94%

Quadrupole phonons in the cadmium isotopes

et al. 2018

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A key question concerning the spherical-vibrator attributes of states in Cadmium isotopes is addressed by means of a boson Hamiltonian encompassing U(5) partial dynamical symmetry. The U(5) symmetry is preserved in a segment of the spectrum and is broken in particular non-yrast states, and the resulting mixing with the intruder states is small. The vibrational character is thus maintained in the majority of low-lying normal states, as observed in 110 Cd.

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Algebraic benchmark for prolate-oblate coexistence in nuclei

Cited by 30 publications

References 53 publications

Aspects of Shape Coexistence in the Geometric Collective Model of Nuclei

Aspects of Shape Coexistence in the Geometric Collective Model of Nuclei

Partial dynamical symmetries and shape coexistence in nuclei

Quadrupole phonons in the cadmium isotopes

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