Quest of shape coexistence in Zr isotopes

Abstract

Background: The mass region with A ≈ 100 and Z ≈ 40 is known to experience a sudden onset of deformation. The presence of the subshell closure Z = 40 makes feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder states could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region.Purpose: The aim of this work is to describe excitation energies, transition rates, radii, and twoneutron separation energies for the even-even 94−110 Zr nuclei and, moreover, to obtain information about wave functions and deformation.Method: The interacting boson model with configuration mixing will be the framework to study the even-even Zr nuclei, considering only two types of configurations: 0particle-0hole and 2particle-2hole excitations. On one hand, the parameters appearing in the Hamiltonian and in the E2 transition operator are fixed trough a least-squares fit to the whole available experimental information. On the other hand, once the parameters have been fixed, the calculations allow to obtain a complete set of observables for the whole even-even Zr chain of isotopes.Results: Spectra, transition rates, radii, ρ 2 (E0), and two-neutron separation energies have been calculated and a good agreement with the experimental information has been obtained. Moreover, a detailed study of the wave function has been conducted and mean-field energy surfaces and deformation have been computed too.Conclusions: The importance of shape coexistence has been shown to correctly describe the A ≈ 100 mass area for even-even Zr nuclei. This work confirmed the rather spherical nature of the ground state of 94−98 Zr and its deformed nature for 100−110 Zr isotopes. The sudden onset of deformation in 100 Zr is owing to the rapid lowering of a deformed (intruder) configuration which is high-lying in lighter isotopes. 21.60.Fw

Subtle connection between shape coexistence and quantum phase transition: The Zr case

“…This approach has been used successfully for describing the spectroscopic properties of Pt [10,11,51], Hg [52,53], Po [12,13], and Zr isotopes [41,54]. The good reproduction of the available experimental data justify the use of only 0p-0h and 2p-2h excitations in the previous cited works.…”

“…The way to do so has been extensively discussed in great detail in Ref. [41] and in an abridged way in Section IV. In According to the previous figures, it is a logical step to assume that Zr undergoes a QPT for A ≈ 100 being possible to define an order parameter ( Fig.…”

“…One can easily compute this energy surfaces once the parameters of the Hamiltonian are given. In our case we use the ones obtained in [41].…”

“…InFig. 5(a) the experimental and theoretical values (see Section IV and[41]) of the nuclear radii are presented with A = 90 taken as the reference nucleus. This observable is related with the evolution of the order parameter and it shows a sudden increase at A = 100.…”

Intertwined quantum phase transitions in the Zr isotopes

“…The 40 Zr isotopes have been recently the subject of several experimental investigations [9][10][11][12][13][14][15] and theoretical studies, including mean-field based methods [16][17][18], the Monte-Carlo shell-model (MCSM) [19] and algebraic methods [8,20]. We adapt here the algebraic approach of the Interacting Boson Model (IBM) [21], with bosons representing valence nucleon pairs counted from the nearest closed shells.…”