Zr Isotopes as a region of intertwined quantum phase transitions

TL;DR

This paper investigates the complex structural evolution of zirconium isotopes using the interacting boson model with configuration mixing, revealing intertwined quantum phase transitions involving shape changes and configuration crossings, consistent with extensive experimental data.

Contribution

It provides a detailed analysis of IQPTs in zirconium isotopes, demonstrating the coexistence of Type I and Type II quantum phase transitions within a unified framework.

Findings

Identification of Type I QPTs from weakly deformed to gamma-unstable shapes.

Observation of Type II QPTs between normal and intruder configurations.

Excellent agreement between model calculations and experimental data.

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 $A\approx100$. 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.