arXiv subjects

A. Leviatan

Publications and source records attributed to A. Leviatan.

At least 19 recordsLinked to original sources

arXiv2025

Quantum and classical analyses of intertwined phase transitions in odd-mass Nb isotopes

Quantum phase transitions (QPTs) in odd-mass Nb isotopes are investigated in the framework of the interacting boson-fermion model with configuration mixing. A quantum analysis reveals a Type I QPT (gradual shape-evolution within the intruder configuration) superimposed on a Type II QPT (abrupt crossing of normal and intruder states), thus demonstrating the occurrence of intertwined QPTs. A classical analysis highlights the implications for the single particle motion in the deformed field generated by the even-even Zr cores.

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arXiv2025

Geometry of Configuration Mixing in Bose-Fermi Systems

A geometric interpretation for an algebraic interacting boson-fermion model with configuration mixing is presented. The formalism is based on an extended Bose-Fermi matrix coherent states and is applied to gain insight on intertwined quantum shape-phase transitions and shape coexistence in odd-mass Nb nuclei.

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arXiv2025

Vibrational structure and symmetry in $^{110-116}$Cd

We show that a vibrational interpretation and good U(5) symmetry are maintained for the majority of low-lying normal states in $^{110,112,114,116}$Cd isotopes, consistent with the empirical data. The observed deviations from this paradigm are properly treated by an interacting boson model Hamiltonian which breaks the U(5) symmetry in selected non-yrast states, while securing a weak mixing with coexisting SO(6)-like intruder states. The results demonstrate the relevance of the U(5) partial dynamical symmetry notion to this series of isotopes.

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arXiv2024

Intertwined Quantum Phase Transitions in Bose and Bose-Fermi Systems

Pronounced structural changes within individual configurations (Type I QPT), superimposed on an abrupt crossing of these configurations (Type II QPT), define the notion of intertwined quantum phase transitions (QPTs). We discuss and present evidence for such a scenario in finite Bose and Bose-Fermi systems. The analysis is based on algebraic models with explicit configuration mixing, where the two types of QPTs describe shape-phase transitions in-between different dynamical symmetries and shape-coexistence with crossing.

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arXiv2023

Intertwined quantum phase transitions in odd-mass Nb isotopes

A detailed analysis of odd-mass Nb isotopes, in the framework of the interacting boson-fermion model with configuration mixing, discloses the effects of an abrupt crossing of states in normal and intruder configurations (Type~II QPT), on top of which superimposed a gradual evolution from spherical- to deformed-core shapes within the intruder configuration (Type~I QPT). The pronounced presence of both types of QPTs demonstrates, for the first time, the occurrence of intertwined QPTs in odd-mass nuclei.

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arXiv2023

Persistent vibrational structure in $^{110-116}$Cd

The empirical spectra and $E2$ decay rates in $^{110,112,114,116}$Cd are shown to be consistent with a vibrational interpretation for low-lying normal states, coexisting with a single deformed $γ$-soft band of intruder states. The observed deviations from this paradigm show up in particular non-yrast states, which are properly described by a Hamiltonian with U(5) partial dynamical symmetry. The latter is characterized by a good (broken) symmetry in most (in selected) normal states, weakly coupled to intruder states.

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arXiv2022

Zr Isotopes as a region of intertwined quantum phase transitions

The zirconium isotopes with $A=$ 92$-$110 have one of the most complicated evolution of structure in the nuclear chart. In order to understand the structural evolution of these isotopes, we carry a detailed calculation in a definite symmetry-based framework, the interacting boson model with configuration mixing (IBM-CM). We compare our calculation to a large range of experimental data, such as energy levels, two neutron separation energies, $E2$ and $E0$ transition rates, isotope shifts and magnetic moments. The structural evolution of the low lying spectra of these isotopes is explained using the notion of intertwined quantum phase transitions (IQPTs), for which a QPT involving a crossing of two configurations (Type II) is accompanied by a QPT involving a shape evolution of each configuration separately (Type I). In our study, we find the occurrence of Type I QPT within the intruder configuration, changing from weakly deformed to prolate deformed and finally to $γ$-unstable, associated with the U(5), SU(3) and SO(6) dynamical symmetry limits of the IBM, respectively. Alongside the Type I QPT, we also find the occurrence of Type II QPT between the normal and intruder configurations, where both Types I and II have a critical-point near $A\approx100$. The good agreement of our calculation with the vast empirical data along the chain of isotopes demonstrates the relevance of IQPTs to the zirconium isotopes, and can serve as a case study to set path for new investigations of IQPTs in other nuclei and other physical systems.

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arXiv2021

Linking partial dynamical symmetry to nuclear energy density functionals

We use self-consistent mean-field methods in combination with the interacting boson model (IBM) of nuclei, to establish a linkage between universal energy density functionals (EDFs) and partial dynamical symmetry (PDS). An application to $^{168}$Er shows that IBM Hamiltonians derived microscopically from known nonrelativistic and relativistic EDFs in this region, conform with SU(3)-PDS.

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arXiv2021

Partial dynamical symmetry from energy density functionals

We show that the notion of partial dynamical symmetry is robust and founded on a microscopic many-body theory of nuclei. Based on the universal energy density functional framework, a general quantal boson Hamiltonian is derived and shown to have essentially the same spectroscopic character as that predicted by the partial SU(3) symmetry. The principal conclusion holds in two representative classes of energy density functionals: nonrelativistic and relativistic. The analysis is illustrated in application to the axially-deformed nucleus $^{168}$Er.

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arXiv2021

Tests of collectivity in $^{98}$Zr by absolute transition rates

Lifetimes of low-spin excited states in $^{98}$Zr were measured using the recoil-distance Doppler-shift technique and the Doppler-shift attenuation method. The nucleus of interest was populated in a $^{96}$Zr($^{18}$O,$^{16}$O)$^{98}$Zr two-neutron transfer reaction at the Cologne FN Tandem accelerator. Lifetimes of six low-spin excited states, of which four are unknown, were measured. The deduced $B(E2)$ values were compared with Monte Carlo shell model and interacting boson model with configuration mixing calculations. Both approaches reproduce well most of the data but leave challenging questions regarding the structure of some low lying states.

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arXiv2020

SU(3) partial dynamical symmetry and nuclear shapes

We consider several variants of SU(3) partial dynamical symmetry in relation to quadrupole shapes in nuclei. Explicit construction of Hamiltonians with such property is presented in the framework of the interacting boson model (IBM), including higher order terms, and in its proton-neutron extension (IBM-2). The cases considered include a single prolate-deformed shape with solvable ground and $γ$ or $β$ bands, coexisting prolate-oblate shapes with solvable ground bands, and aligned axially-deformed proton-neutron shapes with solvable symmetric ground and $γ$ bands and mixed-symmetry scissors and $γ$ bands.

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arXiv2020

Quantum catastrophes from an algebraic perspective

We study the properties of quantum cusp and butterfly catastrophes from an algebraic viewpoint. The analysis employs an interacting boson model Hamiltonian describing quantum phase transitions between specific quadrupole shapes by interpolating between two incompatible dynamical symmetry limits. The classical properties are determined by using coherent states to construct the complete phase diagrams associated with Landau potentials exhibiting such catastrophes.The quantum properties are determined by analyzing the spectra, transition rates and symmetry character of the eigenstates of critical Hamiltonians.

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arXiv2020

Interplay between shape-phase transitions and shape coexistence in the Zr isotopes

We investigate the evolution of structure in the zirconium isotopes where one of the most complex situations encountered in nuclear physics occurs. We demonstrate the role of two concurrent types of quantum phase transitions, sharing a common critical point. The first type, involves an abrupt crossing of coexisting normal and intruder configurations. The second type, involves a gradual shape-phase transition within the intruder configuration, changing from weakly-deformed to prolate-deformed and finally to gamma-unstable. Evidence for this scenario is provided by a detailed comparison with experimental data, using a definite algebraic framework.

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arXiv2019

Multiple quantum phase transitions in the Zr isotopes

We present a detailed analysis of spectra and other observables for the entire chain of Zr isotopes, from neutron number 52 to 70, in the framework of the interacting boson model with configuration mixing. The results suggest a remarkable interplay of multiple quantum phase transitions (QPTs). One type of QPT involves an abrupt crossing of normal and intruder configurations, superimposed on a second type of QPT involving gradual shape-changes within each configuration.

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arXiv2019

Intertwined quantum phase transitions in the Zr chain

We introduce the notion of intertwined quantum phase transitions (IQPTs), for which a crossing of two configurations coexists with a pronounced shape-evolution of each configuration. A detailed analysis in the framework of the interacting boson model with configuration mixing, provides evidence for this scenario in the Zr isotopes. The latter exhibit a normal configuration which remains spherical along the chain, but exchanges roles with an intruder configuration, which undergoes first a spherical to prolate-deformed [U(5)$\to$SU(3)] QPT and then a crossover to $γ$-unstable [SU(3)$\to$SO(6)].

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arXiv2019

Intertwined Quantum Phase Transitions in the Zr Isotopes

We explore the situation of intertwined quantum phase transitions (IQPTs), for which a QPT involving a crossing of two configurations is accompanied by a shape evolution of each configuration with its own separate QPT. We demonstrate the relevance of IQPTs to the Zr isotopes, with such coexisting Type I and Type II QPTs, and ground state shapes changing from spherical to prolate axially deformed and finally to gamma-unstable. Evidence for this scenario is provided by a detailed comparison with experimental data, using a definite symmetry-based conceptual framework.

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arXiv2019

Dynamical Symmetries and Beyond: Lessons and Advances

A central theme in Iachello's quest for understanding simple ordered patterns in complex quantum systems, is the concept of dynamical symmetry. Relying on his seminal contributions, we present further generalization of this notion to that of partial dynamical symmetry (PDS), for which solvability and good quantum numbers are maintained by only a subset of states. Hamiltonians with a single PDS and multiple PDSs are constructed explicitly and their relevance to nuclear structure is discussed.

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arXiv2018

Partial dynamical symmetry and the phonon structure of cadmium isotopes

The phonon structure and spectral properties of states in $^{110}$Cd are addressed by including proton excitations in the phonon basis and exploiting a partial dynamical symmetry that mixes only certain classes of states and maintains the vibrational character in the majority of normal states.

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