$\beta$-decay half-lives as an indicator of shape-phase transition in neutron-rich Zr isotopes with particle-vibration coupling effect

TL;DR

This study shows that $eta$-decay half-lives can serve as indicators of shape-phase transitions in neutron-rich Zr isotopes, with theoretical models predicting observable changes at shape changes.

Contribution

It introduces a combined RPA and PVC approach to link $eta$-decay half-lives with nuclear shape transitions in Zr isotopes, highlighting the impact of shape changes on decay properties.

Findings

Shorter half-lives at shape transitions.

PVC effect reduces half-lives, especially in spherical configurations.

Sudden half-life shortening signals shape change.

Abstract

[Background] $\beta$-decay half-life is sensitive to the shell structure near the Fermi levels. Nuclear deformation thus impacts the $\beta$-decay properties. [Purpose] A first-order shape-phase transition in neutron-rich Zr isotopes is predicted by some models. We investigate the $\beta$-decay half-lives of neutron-rich nuclei around $^{110}$Zr, where the shape-phase transition is predicted to occur, to see if the $\beta$-decay half-life can be an indicator of the shape changes. [Method] The proton-neutron quasiparticle random-phase approximation (RPA) is adopted to calculate the Gamow-Teller transitions. In addition, we apply the quasiparticle phonon-vibrational coupling (PVC) to consider the phonon couplings. [Results] The spherical and oblate configurations give similar half-lives but shorter ones than the prolate configuration at the RPA level. The PVC effect further reduces the half-lives in general, but the effect is smaller for the deformed configuration than that for the spherical one. As a result, it makes the shape change from the oblate configuration to the spherical configuration visible. Therefore, a sudden shortening of $\beta$-decay half-lives is always found at the nuclear shape changes. [Conclusions] $\beta$-decay half-life is an indicator of the shape-phase transition. The shape mixing and the roles of the triaxial deformation are subject to study in the future.