First-forbidden continuum- and bound-state β^--decay rates of bare ²⁰⁵Hg⁸⁰⁺ and ²⁰⁷Tl⁸¹⁺ ions

We analyze the decay rates λ_βc^- and λ_βb^- of the continuum- and bound-state β^--decays for bare ²⁰⁵Hg⁸⁰⁺ and ²⁰⁷Tl⁸¹⁺ ions. For the ratio of the decay rates R_b/c=λ_βb^-/λ_βc^- we obtain the values R_b/c=0.161 and R_b/c=0.190 for bare ²⁰⁵Hg⁸⁰⁺ and ²⁰⁷Tl⁸¹⁺ ions, respectively. The theoretical value of the ratio R_b/c=0.190 for the decays of ²⁰⁷Tl⁸¹⁺ agrees well with the experimental data R_b/c^exp=0.188(18), obtained at GSI. The theoretical ratio R_b/c=0.161 for ²⁰⁵Hg⁸⁰⁺ is about 20% smaller than the experimental value R_b/c^exp=0.20(2), measured recently at GSI. We give arguments that the nuclear structure of the nuclei in the ²⁰⁵Hg⁸⁰⁺→ ²⁰⁵Tl⁸¹⁺ transition cannot provide such an enhancement of the ratio. We estimate the values of the continuum- and bound-state β^--decay rates of the bare ²⁰⁵Hg⁸⁰⁺ ions.