Zr Isotopes as a region of intertwined quantum phase transitions

Abstract

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 $\gamma$-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 $A\approx 100$. 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.

25 pages, 20 figures, 6 tables

References in corpus (9)

• Quantum phase transitions in the interacting boson model
• First Measurement of Collectivity of Coexisting Shapes based on Type II Shell Evolution: The Case of ${}^{96}$Zr
• Structural evolution in $A\approx 100$ nuclei within the mapped interacting boson model based on the Gogny energy density functional
• Intertwined Quantum Phase Transitions in the Zr Isotopes
• Evidence for coexisting shapes in ${}^{98}$Zr through lifetime measurements
• The subtle connection between shape coexistence and quantum phase transition. The Zr case
• Consistent description of nuclear charge radii and electric monopole transitions
• Tests of collectivity in ${}^{98}$Zr by absolute transition rates
• Correlating radii and electric monopole transitions of atomic nuclei

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• Configuration mixing and intertwined quantum phase transitions in odd-mass niobium isotopes
• Low-energy structure and $\beta$ decay properties of neutron-rich nuclei in the region of a shape phase transition
• Persistent vibrational structure in ${}^{110-116}$Cd
• Shape evolution in even-mass ${}^{98-104}$Zr isotopes via lifetime measurements using the $\gamma \gamma$-coincidence technique
• Geometry of Configuration Mixing in Bose-Fermi Systems
• Electromagnetic moments in the Sn-Gd region determined within nuclear DFT
• Determination of the spins and parities for the 0${}_4^{+}$ and 0${}_5^{+}$ states in ${}^{100}$Zr
• Intertwined quantum phase transitions in the zirconium and niobium isotopes
• Intertwined quantum phase transitions in odd-mass Nb isotopes
• Microscopic formulation of the interacting boson-fermion model using the nuclear energy density functional
• Quantum and classical analyses of intertwined phase transitions in odd-mass Nb isotopes
• Intertwined Quantum Phase Transitions in Bose and Bose-Fermi Systems