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

Abstract

We investigate the evolution of structure in the zirconium isotopes where one of the most complex situations encountered in nuclear physics occurs. We demonstrate the role of two concurrent types of quantum phase transitions, sharing a common critical point. The first type, involves an abrupt crossing of coexisting normal and intruder configurations. The second type, involves a gradual shapephase transition within the intruder configuration, changing from weakly-deformed to prolate-deformed and finally to gamma-unstable. Evidence for this scenario is provided by a detailed comparison with experimental data, using a definite algebraic framework.

Zr Isotopes as a region of intertwined quantum phase transitions

“…This isotope appears to have features of the so-called X(5) critical-point symmetry [60], similar to the case encountered for neutron number 90 [61][62][63][64][65] for the Nd-Sm-Gd-Dy isotopes, where the symmetry changes from U(5) to SU(3). As 103.0(357) 4) 67 (7) 103 (9) 140 (30) 124 (13) 124 (15) 131( 15) seen in Table I, the normalized energies and E2 transition rates agree well with those of X (5). For the B(E2) ratio involving the 4 + 1 → 2 + 1 transition, the empirical value for 102 Zr is in perfect agreement with the X(5) value 1.58.…”

“…In the present paper, we expand our work from [8,9] and explain how the indication for changes in the content of configuration and the amount of deformation suggests the occurrence of IQPTs in the zirconium isotopes. This is done by presenting a detailed comparison between our calculation and the empirical data for many observables.…”

“…This is achieved in a situation where within the Type II QPT the mixing between the configurations is weak and as a consequence one can identify the Type I QPT within each configuration separately. This results in an intricate interplay of intertwined quantum phase transitions (IQPTs) [8,9], depicted schematically in Fig. 1(c).…”

“…These dramatic structural changes have attracted considerable theoretical and experimental interest in the Zr chain. Different theoretical approaches have studied them, including mean-field based methods, both nonrelativistic [17,18] and relativistic [19], large-scale shellmodel calculations [20,21], the Monte-Carlo shell-model (MCSM) [22] and algebraic models [8,9,23,24]. Recently, several experimental investigations have also come to light [25][26][27][28][29][30][31][32][33], opening the door for understanding the properties of both yrast and non-yrast states.…”

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

“…The study of the possible relationship between shape coexistence and QPT in Zr isotopes has been also carried out in Refs. [76,77], obtaining similar conclusions, although in these works the authors claimed that there is an addition evolution into gamma-unstable shapes in 106 Zr an onwards.…”