Evaluation of bound-state $$\beta ^-$$-decay half-lives of fully ionized atoms

Abstract Bound-state $$\beta ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>β</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:math> -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 $$\beta ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>β</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:math> -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 $$\beta ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>β</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:math> 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 $$\beta ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>β</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:math> -decays of nuclei $$^{163}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>163</mml:mn> </mml:mmultiscripts> </mml:math> Dy, $$^{193}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>193</mml:mn> </mml:mmultiscripts> </mml:math> Ir, $$^{194}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>194</mml:mn> </mml:mmultiscripts> </mml:math> Au, $$^{202}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>202</mml:mn> </mml:mmultiscripts> </mml:math> Tl, $$^{205}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>205</mml:mn> </mml:mmultiscripts> </mml:math> Tl, $$^{215}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>215</mml:mn> </mml:mmultiscripts> </mml:math> At, $$^{222}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>222</mml:mn> </mml:mmultiscripts> </mml:math> Rn, $$^{243}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>243</mml:mn> </mml:mmultiscripts> </mml:math> Am, and $$^{246}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>246</mml:mn> </mml:mmultiscripts> </mml:math> Bk are calculated, where the normal beta-decay is forbidden. In addition, we compute the bound-state $$\beta ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>β</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:math> -decay rates for nuclei $$^{187}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>187</mml:mn> </mml:mmultiscripts> </mml:math> Re, $$^{227}$$