The subtle connection between shape coexistence and quantum phase transition. The Zr case

TL;DR

This paper investigates the rapid shape changes and coexistence phenomena in Zr isotopes, linking them to quantum phase transitions through theoretical modeling of energy surfaces and wave functions.

Contribution

It demonstrates that Zr nuclei exemplify quantum phase transitions driven by configuration crossing and shape coexistence, using the Interacting Boson Model with Configuration Mixing.

Findings

Zr isotopes show rapid shape evolution and coexistence.

Energy surfaces reveal crossing of configurations with different deformations.

Intruder configurations also exhibit quantum phase transition-like behavior.

Abstract

Background: Zr region is characterized by very rapid changes in the ground state structure of the nuclei. In particular, the onset of deformation when passing from $^{98}$Zr to $^{100}$Zr is one of the fastest ever observed in the nuclear chart. It has been probed both experimental and theoretically that certain low-lying excited states of Zr isotopes own different shapes than the ground state. Purpose: We intend to disentangle the interplay between the sudden changes in the ground state shape, i.e., the existence of a quantum phase transition, and the presence in the spectra of coexisting states with very different deformation, i.e., the presence of shape coexistence. Method: We rely on a previous calculation using the Interacting Boson Model with Configuration Mixing (IBM-CM) which reproduces in detail the spectroscopic properties of $^{96-110}$Zr. This IBM-CM calculation allows to compute mean-field energy surfaces, wave functions and any other observable related with the presence of shape coexistence or with a quantum phase transition. Results: We obtain energy surfaces and the equilibrium value of the deformation parameter $\beta$, the U(5) decomposition of the wave functions and the density of states. Conclusions: We confirm that Zr is a clear example of quantum phase transition that originates from the crossing of two configurations with a very different degree of deformation. Moreover, we observe how the intruder configuration exhibits its own evolution which resembles a quantum phase transition too.