Quantum Phase Transition in the Shape of Zr isotopes

Abstract

The rapid shape change in Zr isotopes near neutron number N=60 is identified to be caused by type II shell evolution associated with massive proton excitations to its 0g_{9/2} orbit, and is shown to be a quantum phase transition. Monte Carlo shell-model calculations are carried out for Zr isotopes of N=50-70 with many configurations spanned by eight proton orbits and eight neutron orbits. Energy levels and B(E2) values are obtained within a single framework in good agreement with experiment, depicting various shapes in going from N=50 to 70. The novel coexistence of prolate and triaxial shapes is suggested.

Abrupt shape transition at neutron number N=60 : B(E2) values in SrRégis1, Jolie2, Saed-Samii3 et al. 2017Phys. Rev. C342270View full textAdd to dashboardCite

“…Carlo shell-model (MCSM) calculation has been carried out for Zr isotopes in the N = 50-70 region without truncation of the model space [3]. Level energy and B(E2) values were obtained within a single framework in good agreement with experiments, depicting the abrupt shape transition at N = 60 as a consequence of type II shell evolution involving many proton particle-hole excitations to the g 9/2 orbit [3,4].…”

“…Level energy and B(E2) values were obtained within a single framework in good agreement with experiments, depicting the abrupt shape transition at N = 60 as a consequence of type II shell evolution involving many proton particle-hole excitations to the g 9/2 orbit [3,4]. Let us briefly explain the type II shell evolution.…”

“…1, while discussions with concrete cases can be found in Ref. [3] for Zr isotopes and in Ref. [5] for Ni isotopes.…”

Triaxiality of neutron-rich Ge84,86,88 from low-energy nuclear spectra

“…Furthermore, it was shown that a new region of rigid triaxial deformation should arise around N = 54, which is supported by shell model and beyond-mean-field calculations [28,29], predicting a maximum of triaxiality for the exotic nucleus 86 Ge. Also in the broader mass region above N = 50, new Monte Carlo shell model calculations [30] predict the occurrence of coexisting prolate and triaxial shapes, e.g., leading to a low-lying triaxial band in 110 Zr at N = 70. For proton numbers between Z = 28 and 40, the N = 56,58 subshell closures (2d 5/2 , 3s 1/2 ) may diminish, possibly leading to the occurrence of triaxial structures at smaller values of N as compared to the chain of zirconium isotopes.…”

“…Hence, future more detailed studies of 86 Ge are highly desirable. A study of Effective Single-Particle Energies (ESPEs) like in 110 Zr [30] may shed light on the possibility of the emergence of triaxiality as the result of the bunching of single-particle orbitals. …”