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First-forbidden continuum- and bound-state<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>β</mml:mi><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>-decay rates of bare<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Hg</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>205</mml:mn></mml:mrow></mml:mmultiscripts></mml:math><mml:math xmlns:…
We analyze the decay rates ${\ensuremath{\lambda}}_{{\ensuremath{\beta}}_{c}^{\ensuremath{-}}}$ and ${\ensuremath{\lambda}}_{{\ensuremath{\beta}}_{b}^{\ensuremath{-}}}$ of the continuum- and bound-state ${\ensuremath{\beta}}^{\ensuremath{-}}$-decays for bare $^{205}\mathrm{Hg}$${}^{80+}$ and $^{207}\mathrm{Tl}$${}^{81+}$ ions. For the ratio of the decay rates ${R}_{b/c}={\ensuremath{\lambda}}_{{\ensuremath{\beta}}_{b}^{\ensuremath{-}}}/{\ensuremath{\lambda}}_{{\ensuremath{\beta}}_{c}^{\ensuremath{-}}}$ we obtain the values ${R}_{b/c}=0.161$ and ${R}_{b/c}=0.190$ for bare $^{205}\mathrm{Hg}$${}^{80+}$ and $^{207}\mathrm{Tl}$${}^{81+}$ ions, respectively. The theoretical value of the ratio ${R}_{b/c}=0.190$ for …