Evaluation of bound-state β ⁻-decay half-lives of fully ionized atoms

Bound-state β ⁻ β - -decay is a rare radioactive process where the created electron is trapped in an atomic orbital instead of being emitted. It can be observed in highly ionized atoms in particular when normal beta-decay is energetically forbidden, but bound-state decay is still possible. In this work we present a systematic theoretical study on the bound-state β ⁻ β - -decay of fully ionized atoms where key nuclear inputs include the nuclear shape factor (expressed through ft values) and the lepton phase-space volume function. We present a method to evaluate nuclear shape factor for fully forbidden β ⁻ β - transitions in neutral atoms, from the inverse electron capture process using the Takahashi–Yokoi model and account for the impact of electron capture to different atomic orbitals on the resulting half-lives. Decay rates for bound-state β ⁻ β - -decays of nuclei ¹⁶³ 163 Dy, ¹⁹³ 193 Ir, ¹⁹⁴ 194 Au, ²⁰² 202 Tl, ²⁰⁵ 205 Tl, ²¹⁵ 215 At, ²²² 222 Rn, ²⁴³ 243 Am, and ²⁴⁶ 246 Bk are calculated, where the normal beta-decay is forbidden. In addition, we compute the bound-state β ⁻ β - -decay rates for nuclei ¹⁸⁷ 187 Re, ²²⁷