An improved semi-empirical relationship for $\alpha$-decay half-lives is proposed by introducing a precise radius formula and an analytic expression for preformation probability. By using the improved relationship, the $\alpha$-decay half-lives of 421 nuclei are calculated. It is shown that the accuracy of this semi-empirical relationship is improved significantly compared to its predecessor. Further research shows that it also reproduces the experimental half-lives of the superheavy nuclei well. Last, with the improved formula the $\alpha$-decay half-lives of the $Z=118–121$ isotopes are predicted, which are helpful for future experiments. In addition, there is a prediction of a magic number effect at $N=184$.

• Received 12 September 2016
• Revised 27 October 2016

DOI:https://doi.org/10.1103/PhysRevC.95.014311