arXiv subjects

A. Leviatan

Publications and source records attributed to A. Leviatan.

At least 37 records · Page 2Linked to original sources

arXiv2018

Symmetry-Based Approach to Shape Coexistence in Nuclei

A symmetry-based approach for describing shape-coexistence, is presented in the framework of the interacting boson model of nuclei. It involves a construction of a number-conserving Hamiltonian which preserves the dynamical symmetry of selected bands associated with each shape, while breaking the symmetries in other states. The resulting structure embodies multiple partial dynamical symmetries. The procedure is applied to prolate-oblate and spherical-prolate-oblate coexistence, at and slightly away from the critical points.

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arXiv2018

Quadrupole Phonons in the Cadmium Isotopes

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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arXiv2018

Partial dynamical symmetry and the vibrational structure of Cd isotopes

The recently reported deviations of selected non-yrast states in $^{110}$Cd from the expected spherical-vibrator behaviour, is addressed by means of an Hamiltonian with U(5) partial dynamical symmetry. The latter preserves the U(5) symmetry in a segment of the spectrum and breaks it in other states. The effect of intruder states is treated in the framework of the interacting boson model with configuration mixing.

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arXiv2017

Aspects of Shape Coexistence in the Geometric Collective Model of Nuclei

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.

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arXiv2017

Partial dynamical symmetries and shape coexistence in nuclei

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), ${\overline{\rm SU(3)}}$ 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.

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arXiv2016

Algebraic benchmark for prolate-oblate coexistence in nuclei

We present a symmetry-based approach for prolate-oblate and spherical-prolate-oblate shape coexistence, in the framework of the interacting boson model of nuclei. The proposed Hamiltonian conserves the SU(3) and $\overline{\rm SU(3)}$ symmetry for the prolate and oblate ground bands and the U(5) symmetry for selected spherical states. Analytic expressions for quadrupole moments and $E2$ rates involving these states are derived and isomeric states are identified by means of selection rules.

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arXiv2015

Simultaneous occurrence of distinct symmetries in nuclei

We show that distinct emergent symmetries, such as partial dynamical symmetry and quasi dynamical symmetry, can occur simultaneously in the same or different eigenstates of the Hamiltonian. Implications for nuclear spectroscopy in the rare-earth region and for first-order quantum phase transitions between spherical and deformed shapes, are considered.

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arXiv2015

Partial Dynamical Symmetry in Odd-Mass Nuclei

Spectral features of the odd-mass nucleus $^{195}$Pt are analyzed by means of an interacting boson-fermion Hamiltonian with SO(6) partial dynamical symmetry. For the latter, selected eigenstates are solvable and preserve the symmetry exactly, while other states are mixed. The analysis constitutes a first example of this novel symmetry construction in a mixed Bose-Fermi system.

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arXiv2015

Symmetry Remnants in the Face of Competing Interactions in Nuclei

Detailed description of nuclei necessitates model Hamiltonians which break most dynamical symmetries. Nevertheless, generalized notions of partial and quasi dynamical symmetries may still be applicable to selected subsets of states, amidst a complicated environment of other states. We examine such scenarios in the context of nuclear shape-phase transitions.

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arXiv2015

Partial dynamical symmetry in Bose-Fermi systems

We generalize the notion of partial dynamical symmetry (PDS) to a system of interacting bosons and fermions. In a PDS, selected states of the Hamiltonian are solvable and preserve the symmetry exactly, while other states are mixed. As a first example of such novel symmetry construction, spectral features of the odd-mass nucleus $^{195}$Pt are analyzed.

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arXiv2014

Partial and quasi dynamical symmetries in quantum many-body systems

We introduce the notions of partial dynamical symmetry (PDS) and quasi dynamical symmetry (QDS) and demonstrate their relevance to nuclear spectroscopy, to quantum phase transitions and to mixed systems with regularity and chaos. The analysis serves to highlight the potential role of PDS and QDS towards understanding the emergent "simplicity out of complexity" exhibited by complex many-body systems.

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arXiv2014

Partial dynamical symmetry and odd-even staggering in deformed nuclei

Partial dynamical symmetry (PDS) is shown to be relevant for describing the odd-even staggering in the $γ$-band of $^{156}$Gd while retaining solvability and good SU(3) symmetry for the ground and $β$ bands. Several classes of interacting boson model Hamiltonians with SU(3) PDS are surveyed.

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arXiv2014

First-order quantum phase transitions: test ground for emergent chaoticity, regularity and persisting symmetries

We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT between spherical and deformed shapes, associated with its U(5) and SU(3) dynamical symmetry limits. A classical analysis of the intrinsic dynamics reveals a rich but simply-divided phase space structure with a Hénon-Heiles type of chaotic dynamics ascribed to the spherical minimum and a robustly regular dynamics ascribed to the deformed minimum. The simple pattern of mixed but well-separated dynamics persists in the coexistence region and traces the crossing of the two minima in the Landau potential. A quantum analysis discloses a number of regular low-energy U(5)-like multiplets in the spherical region, and regular SU(3)-like rotational bands extending to high energies and angular momenta, in the deformed region. These two kinds of regular subsets of states retain their identity amidst a complicated environment of other states and both occur in the coexistence region. A symmetry analysis of their wave functions shows that they are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), respectively. The pattern of mixed but well-separated dynamics and the PDS or QDS characterization of the remaining regularity, appear to be robust throughout the QPT. Effects of kinetic collective rotational terms, which may disrupt this simple pattern, are considered.

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arXiv2014

Linking partial and quasi dynamical symmetries in rotational nuclei

Background: Quasi dynamical symmetries (QDS) and partial dynamical symmetries (PDS) play an important role in the understanding of complex systems. Up to now these symmetry concepts have been considered to be unrelated. Purpose: Establish a link between PDS and QDS and find an emperical manifestation. Methods: Quantum number fluctuations and the intrinsic state formalism are used within the framework of the interacting boson model of nuclei. Results: A previously unrecognized region of the parameter space of the interacting boson model that has both O(6) PDS (purity) and SU(3) QDS (coherence) in the ground band is established. Many rare-earth nuclei approximately satisfying both symmetry requirements are identified. Conclusions: PDS are more abundant than previously recognized and can lead to a QDS of an incompatible symmetry.

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arXiv2014

Order, Chaos and Quasi Symmetries in a First-Order Quantum Phase Transition

We study the competing order and chaos in a first-order quantum phase transition with a high barrier. The boson model Hamiltonian employed, interpolates between its U(5) (spherical) and SU(3) (deformed) limits. A classical analysis reveals regular (chaotic) dynamics at low (higher) energy in the spherical region, coexisting with a robustly regular dynamics in the deformed region. A quantum analysis discloses, amidst a complicated environment, persisting regular multiplets of states associated with partial U(5) and quasi SU(3) dynamical symmetries.

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arXiv2013

Partial dynamical symmetry as a selection criterion for many-body interactions

We propose the use of partial dynamical symmetry (PDS) as a selection criterion for higher-order terms in situations when a prescribed symmetry is obeyed by some states and is strongly broken in others. The procedure is demonstrated in a first systematic classification of many-body interactions with SU(3) PDS that can improve the description of deformed nuclei. As an example, the triaxial features of the nucleus 156Gd are analyzed.

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arXiv2012

Interplay of order and chaos across a first-order quantum shape-phase transition in nuclei

We study the nature of the dynamics in a first-order quantum phase transition between spherical and prolate-deformed nuclear shapes. Classical and quantum analyses reveal a change in the system from a chaotic Hénon-Heiles behavior on the spherical side into a pronounced regular dynamics on the deformed side. Both order and chaos persist in the coexistence region and their interplay reflects the Landau potential landscape and the impact of collective rotations.

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arXiv2012

From Exact to Partial Dynamical Symmetries: Lessons From the Interacting Boson Model

We exploit the rich algebraic structure of the interacting boson model to explain the notion of partial dynamical symmetry (PDS), and present a procedure for constructing Hamiltonians with this property. We demonstrate the relevance of PDS to various topics in nuclear spectroscopy, including K-band splitting, odd-even staggering in the gamma-band and anharmonicity of excited vibrational bands. Special emphasis in this construction is paid to the role of higher-order terms.

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