Competition between Allowed and First-Forbidden $\beta$ Decay: The Case of ${}^{208}\mathrm{Hg}\to {}^{208}\mathrm{Tl}$

The $\beta$ decay of ${}^{208}\mathrm{Hg}$ into the one-proton hole, one neutron-particle ${{}_{81}{}^{208}\mathrm{Tl}}_{127}$ nucleus was investigated at CERN-ISOLDE. Shell-model calculations describe well the level scheme deduced, validating the proton-neutron interactions used, with implications for the whole of the $N>126$, $Z<82$ quadrant of neutron-rich nuclei. While both negative and positive parity states with spin 0 and 1 are expected within the $Q_{\beta }$ window, only three negative parity states are populated directly in the $\beta$ decay. The data provide a unique test of the competition between allowed Gamow-Teller and Fermi, and first-forbidden $\beta$ decays, essential for the understanding of the nucleosynthesis of heavy nuclei in the rapid neutron capture process. Furthermore, the observation of the parity changing $0^{+}\to 0^{-}\beta$ decay where the daughter state is core excited is unique, and can provide information on mesonic corrections of effective operators.

Figure 1

(a) $\gamma$-ray spectrum measured at the implantation position. Daughter nuclei are indicated. The transmission of $A=208$ molecules ${}^{206}\mathrm{Hg}{{}^1\mathrm{H}}_2$ and ${}^{192}\mathrm{Au}{}^{16}\mathrm{O}$ resulted in transitions in ${}^{206}\mathrm{Tl}$, ${}^{192}\mathrm{Pt}$, and ${}^{192}\mathrm{Au}$. Some ${}^{207}\mathrm{Hg}$, decaying into ${}^{207}\mathrm{Tl}$ was also transmitted. (b) $\beta$-gated spectrum. (c) $\beta$-gated spectrum in coincidence with a 453 keV $\gamma$-ray transition, providing a clean ${}^{208}\mathrm{Tl}$ spectrum.

Figure 2

Proposed level scheme of ${}^{208}\mathrm{Tl}$ from the present work. The long-lived states are in bold. The widths of the arrows represent the transition intensity, with the black and white parts corresponding to the $\gamma$ and conversion electon emmissions, respectively. The dominant configurations are indicated.

Figure 3

(a) Lifetime of the isomeric state at $E_x=1807\mathrm{keV}$ in ${}^{208}\mathrm{Tl}$. The time difference between the $\beta$ particle and any of the 221–453 and 221–936 keV $\gamma$-ray pairs is shown. (b) Lifetime of the ${}^{208}\mathrm{Hg}$ ground state determined both from the accumulation and decay phases. Since the former one assumes a constant implantation rate, the value obtained during the exponential decay phase is adopted.

Figure 4

Comparison of experimentally observed states with shell-model calculations. The horizontal lines indicate the theoretical values. The experimental values are denoted by circles (for states observed in the present experiment) and triangles (states from Ref. [20]). Levels with the same dominant configurations are connected. Positive (negative) parity states are shown in red (blue). Black is used for core-excited negative-parity states.