Intertwined quantum phase transitions in the Zr isotopes

Abstract

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.

Quest of shape coexistence in Zr isotopes

“…In the process of finishing this work, we became aware of the publication of another IBM-CM calculation by Gavrielov et al [149] for the even-even Zr isotopes, where the authors have obtained very much the same results as presented here [on energy spectra, B(E2; 2 + 1 → 0 + 1 ), isotopic shifts, and two-neutron separation energies], although they claim that the heavier Zr isotopes own an almost O(6) symmetry, which is differing with the calculations discussed in the present work. The reason for considering 106−110 Zr close to the O(6) symmetry in [149] is mainly based on the presence of a 2 + states near to the energy of the 4 + 1 state, in spite of a experimental value of E(4 + 1 )/E(2 + 1 ) close to 3, which is more in favour of the start of a rotational spectrum. New experimental information in this area will definitively be necessary to disentangle the nature of the heavier Zr isotopes.…”

“…The latter being highlighted by a valley connecting the oblate and prolate sides, exhibiting a shift into a triaxial shape in 110 Zr. The paper that we already mentioned [149] also addressed the topic of triaxial shapes and illustrated this by showing the total energy surfaces, exhibiting a tendency to evolve from a prolate shape (from A = 100 onwards till 106) to move towards the gamma direction in 110 Zr, although these results are not conclusive.…”

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

“…In the present work, we show that these different types of QPTs [23] play a role in the Zr chain, and that in parallel to an abrupt swapping of configurations, each configuration maintains its purity and its own gradual shape-evolution with nucleon number. This situation, referred to as intertwined quantum phase transitions [24], gives rise to an intricate interplay between shape-phase transitions and shape coexistence in nuclei. The notion of intertwined quantum phase transitions is illustrated schematically in Fig.…”

Intertwined quantum phase transitions in the Zr chain

“…In the present contribution, we explore a situation where in parallel to the crossing, each configuration maintains its purity and its own shape-evolution with nucleon number. We refer to such a scenario as intertwined quantum phase transitions (IQPTs) in the sense that Type I and Type II coexist, and show empirical evidence for it in the Zr chain [5].…”

“…Data taken from AME2016 [23]. Adapted from [5]. the replacement γ-unstable → triaxial and the inclusion of more than two configurations in the MCSM.…”