Calculations of bound-state $\beta^-$-decay half-lives of highly ionized $^{163}$Dy$^{66+}$, $^{187}$Re$^{75+}$ and $^{205}$Tl$^{81+}$

TL;DR

This paper introduces a new theoretical method combining the Takahashi-Yokoi model and a projected shell model to accurately calculate bound-state beta-decay half-lives of highly ionized atoms across a range of nuclear masses.

Contribution

It presents a systematic approach to compute bound-state beta-decay half-lives for various nuclei, including odd and even mass cases, with improved accuracy over previous models.

Findings

Calculated half-lives for $^{163}$Dy$^{66+}$ and $^{187}$Re$^{75+}$ match experimental data within a factor of two and four.

Predicted the half-life of $^{205}$Tl$^{81+}$ as 58 days without quenching and 305 days with quenching.

Method successfully accounts for both allowed and first-forbidden transitions in highly ionized nuclei.

Abstract

We propose a theoretical method to calculate the bound-state $\beta$-decay half-lives of highly-ionized atoms, which is based on the combination of the Takahashi-Yokoi model and our recently-developed projected shell model that can take into account both allowed and first-forbidden transitions of nuclear $\beta$ decay. Three examples that are of much experimental interests, $^{163}$Dy$^{66+}$, $^{187}$Re$^{75+}$ and $^{205}$Tl$^{81+}$ are taken for calculations. The ground and low-lying states of related nuclei are described reasonably. The bound-state $\beta$-decay half-lives of $^{163}$Dy$^{66+}$ and $^{187}$Re$^{75+}$ are described within a factor of two and four by our calculations without and with the quenching factors in allowed and first-forbidden transitions. The bound-state $\beta$-decay half-life of the last $s$-process branching point $^{205}$Tl$^{81+}$ is predicted to be 58 and 305 days for cases without and with the quenching factors in calculations. The presented method provides a theoretical way to calculate systematically the bound-state $\beta$-decay half-lives of nuclei from light to heavy ones including odd-mass and even-mass cases for the first time.