Empirical systematics of spontaneous fission half-lives of heavy and superheavy nuclei

A new phenomenological approach is presented for predicting the spontaneous fission half-lives of actinides and superheavy nuclei. A linear correlation is found between the decimal logarithm of the spontaneous fission half-lives ${log}_{10}{T}_{1/2}^{\text{SF}}$ and the energy release ${Q}_{\ensuremath{\alpha}}$ of alpha decay for nuclei with the same neutron excess $N\ensuremath{-}Z$ and atomic numbers in the range $90\ensuremath{\le}Z\ensuremath{\le}102$. This correlation allows us to propose a semiempirical formula for predicting the spontaneous fission half-lives of even-even nuclei, taking into account both the ${Q}_{\ensuremath{\alpha}}$ and $N\ensuremath{-}Z$. The proposed formula is further extended to predict half-lives for odd-$A$, odd-odd nuclei, and nuclei with $Z\ensuremath{\ge}103$. A detailed comparison of the predicted half-lives calculated using the microscopic-macroscopic and self-consistent microscopic models and the new semiempirical formula is given. The competition between alpha decay and spontaneous fission is analyzed. The existence of a fundamental relationship between spontaneous fission and alpha-decay processes is discussed.