The recently measured probabilities of the $\beta$-delayed fission for ${}^{178,180}$Tl are used to deduce the fission-barrier heights of the daughter isotopes ${}^{178,180}$Hg, undergoing low-energy fission. Four alternative $\beta$-decay strength functions and four variants of the statistical model of de-excitation of the daughter nucleus are used to determine the fission-barrier height for ${}^{180}$Hg. Depending on the choice of the model, the deduced fission-barrier heights appear to be between 10$\%$ and 40$\%$ smaller than theoretical estimates. This observation is verified also for fission-barrier heights extracted using the probability of $\beta$-delayed fission of ${}^{178}$Tl. The spread in extracted fission-barrier heights results mainly from uncertainties in the magnitude of the pairing gap at the saddle configuration.

• Received 25 June 2012

DOI:https://doi.org/10.1103/PhysRevC.86.024308