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

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 ${}^{110}\mathrm{Zr}$, 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-vibration 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.

Figure 1

Potential energy surface (zero at the spherical configuration) of ${}^{112–118}\mathrm{Zr}$ obtained by employing the SkM* functional.

Figure 2

$\beta$-decay half-lives of the Zr isotopes obtained by employing the SkM* (upper) and SLy4 (lower) functionals. Filled symbols indicate the lowest energy configuration. The calculated half-lives are compared with the experimental data [42] and the $\mathrm{FRDM}+\mathrm{QRPA}$ calculation [43].

Figure 3

Distributions of the partial-decay rates in ${}^{112}\mathrm{Zr}$ (upper) and ${}^{114}\mathrm{Zr}$ (lower) as functions of the excitation energy with respect to the ground state of the mother nucleus. The RPA results for the prolate, oblate, and spherical configurations are shown together with the QPVC result for the spherical configuration. The RPA results are smeared by the Lorentzian function with a width of $\mathrm{\Gamma }=0.4$ MeV.

Figure 4

Distributions of (a) quadrupole and (b) octupole strengths in ${}^{114}\mathrm{Zr}$ calculated within the framework of Secs. 2a and 2b.