The Royer formulas are often used to calculate the $\alpha$-decay half-lives [G. Royer, J. Phys. G 26, 1149 (2000); Nucl. Phys. A 848, 279 (2010)]. In recent years, the amount of experimental data on $\alpha$ decay has increased and these formulas have been examined again. They describe precisely the favored $\alpha$ decays. For unfavored decays, they are less accurate and important deviations may occur between the calculations and experimental data. The underlying physics of this phenomenon has been revealed and an improved formula with only eight parameters is proposed. This formula takes into account both the blocking effect of unpaired nucleons and the contribution of centrifugal potential. Compared with the original formulas and other improvements, our new formula is more simple to use and more accurate. Encouraged by this, the $\alpha$-decay half-lives of even-even nuclei and odd-$A$ nuclei with $Z=117$, 118, 119, and 120 are predicted using our improved formula and the universal decay law [C. Qi et al., Phys. Rev. Lett. 103, 072501 (2009)] with the extrapolated $Q_{\alpha }$ of the WS3+ mass model [N. Wang and M. Liu, Phys. Rev. C 84, 051303(R) (2011)]. The predictions of these two formulas are consistent. However, for ${}^{293}\mathrm{Ts}$ and ${}^{294}\mathrm{Og}$, predicted $\alpha$-decay half-lives by our improved formula show better agreement with experimental data, indicating that predictions by our improved formula are more reliable and useful for future new superheavy elements and isotopes experimental assignments and identifications. Meanwhile, the features of predicted $\alpha$-decay energy and half-lives imply that $N=184$ is the next neutron magic number after $N=126$.

• Received 8 January 2020
• Accepted 24 February 2020

DOI:https://doi.org/10.1103/PhysRevC.101.034307