Investigation of the $\Delta n = 0$ selection rule in Gamow-Teller transitions: The $\beta$-decay of $^{207}$Hg

Gamow-Teller $\beta$ decay is forbidden if the number of nodes in the radial wave functions of the initial and final states is different. This $\Delta n=0$ requirement plays a major role in the $\beta$ decay of heavy neutron-rich nuclei, affecting the nucleosynthesis through the increased half-lives of nuclei on the astrophysical $r$-process pathway below both $Z=50$ (for $N>82$ ) and $Z=82$ (for $N>126$). The level of forbiddenness of the $\Delta n=1\ \nu 1g_{9/2} \rightarrow \pi0g_{7/2}$ transition has been investigated from the $\beta^-$ decay of the ground state of $^{207}$Hg into the single-proton-hole nucleus $^{207}$Tl in an experiment at the ISOLDE Decay Station. From statistical observational limits on possible $\gamma$-ray transitions depopulating the $\pi 0g_{7/2}^{−1}$ state in $^{207}$Tl, an upper limit of $3.9 \times 10^{−3}$% was obtained for the probability of this decay, corresponding to log$⁡ft > 8.8$ within a 95% confidence limit. This is the most stringent test of the $\Delta n=0$ selection rule to date.