$\alpha$-decay for superheavy nucleus: The alpha decay energy to the one-fourth power

Abstract

Recently, Sobhani and Luo \cite{sobhani2025unified} proposed a new empirical formula for $\alpha$ decay based on the $Q_{\alpha }^{-1/4}$ energy dependence, incorporating the proton number $Z$, neutron number $N$, and relative neutron excess $I=(N-Z)/(N+Z)$ as primary parameters. In this work, we extend this model by explicitly including the angular momentum of the emitted $\alpha$ particle and the quadrupole deformation of the daughter nucleus. Using this improved formula to evaluate the $\alpha$-decay half-lives of 400 nuclei yields a root-mean-square (RMS) deviation of 0.97 relative to experimental data. Furthermore, we employ support vector regression (SVR)-taking $Q_{\alpha }^{-1/4}$, $N$, $Z$, angular momentum, and daughter-nucleus deformation as input features-which further reduces the RMS deviation to 0.56. Finally, we apply both the extended formula and the SVR model to predict the $\alpha$-decay half-lives of even-even nuclei with $Z=120$ and $Z=122$. The predicted half-lives show good consistency with those from the Sobhani and Poenaru formulas, and both approaches strongly support $N=184$ as the next neutron magic number.