Semiempirical Formula for Calculating Spontaneous Fission Half-Lives

A new phenomenological approach to predicting spontaneous fission half-lives of actinide and superheavy nuclei is presented. A linear relation between the common logarithm of the spontaneous fission half-life $$\log_{10}T_{1/2}^{\text{SF}}$$ , and the alpha-particle separation energy $$Q_{\alpha}$$ is found for nuclei characterized by a fixed value of the neutron excess $$N-Z$$ and by charge-number values in the range of $$90\leqslant Z\leqslant 102$$ . A semiempirical formula for calculating the spontaneous fission half-life as a function of $$Q_{\alpha}$$ and $$N-Z$$ for even–even nuclei is proposed on the basis of this correlation. This formula is successfully extended to nuclei that have an odd mass number $$A$$ and odd–odd nuclei, as well as to nuclei for which $$Z\geqslant 103$$ . The formula shows good agreement with experimental data, reproducing the half-lives of 111 known nuclei with a mean deviation of about one order of magnitude. The predictions of the new formula are compared with the results based on other empirical formulas and on macroscopic–microscopic and self-consistent microscopic models. The influence of the choice of various mass tables on the accuracy of the predictions is analyzed. The possible fundamental interplay of the spontaneous fission and alpha-decay processes is discussed.