Empirical description of beta-delayed fission partial half-lives

Background: The process of $\ensuremath{\beta}$-delayed fission $(\ensuremath{\beta}\mathrm{DF})$ provides a versatile tool to study low-energy fission in nuclei far away from the $\ensuremath{\beta}$-stability line, especially for nuclei which do not fission spontaneously.Purpose: The aim of this paper is to investigate systematic trends in $\ensuremath{\beta}\mathrm{DF}$ partial half-lives.Method: A semi-phenomenological framework was developed to systematically account for the behavior of $\ensuremath{\beta}\mathrm{DF}$ partial half-lives.Results: The $\ensuremath{\beta}\mathrm{DF}$ partial half-life appears to exponentially depend on the difference between the $Q$ value for $\ensuremath{\beta}$ decay of the parent nucleus and the fission-barrier energy of the daughter (after $\ensuremath{\beta}$ decay) product. Such dependence was found to arise naturally from some simple theoretical considerations.Conclusions: This systematic trend was confirmed for experimental $\ensuremath{\beta}\mathrm{DF}$ partial half-lives spanning over seven orders of magnitude when using fission barriers calculated from either the Thomas-Fermi or the liquid-drop fission model. The same dependence was also observed, although less pronounced, when comparing to fission barriers from the finite-range liquid-drop model or the Thomas-Fermi plus Strutinsky integral method.