Calculations of bound-state β⁻-decay half-lives of highly ionized ¹⁶³Dy⁶⁶⁺, ¹⁸⁷Re⁷⁵⁺ and ²⁰⁵Tl⁸¹⁺

We propose a theoretical method to calculate the bound-state β-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 β decay. Three examples that are of much experimental interests, ¹⁶³Dy⁶⁶⁺, ¹⁸⁷Re⁷⁵⁺ and ²⁰⁵Tl⁸¹⁺ are taken for calculations. The ground and low-lying states of related nuclei are described reasonably. The bound-state β-decay half-lives of ¹⁶³Dy⁶⁶⁺ and ¹⁸⁷Re⁷⁵⁺ 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 β-decay half-life of the last s-process branching point ²⁰⁵Tl⁸¹⁺ 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 β-decay half-lives of nuclei from light to heavy ones including odd-mass and even-mass cases for the first time.