The analysis of predictability of $\alpha$ -decay half-life formulae and the $\alpha$ partial half-lives of some exotic nuclei

Abstract

The predictabilities of the three $\alpha$ -decay half-life formulae, the Royer GLDM, the Viola-Seaborg and the Sobiczewski-Parkhomenko formulae, have been evaluated by developing a method based on the ansatz of standard experimental benchmarking. The coefficients of each formula were re-derived using the reliable data of the $\alpha$ -standards nuclei. The modified formulae that resulted were used to evaluate the accuracies of the formulae towards the prediction of half-lives of a set of nuclides with well-studied $\alpha$ spectroscopic data as well as a set of exotic $\alpha$ emitters. Further, a simple linear optimisation of the modified formulae allowed adjustments for the insufficient statistics of the primary data set without changing the modified formulae. While the three modified formulae showed equivalent results for all the medium heavy nuclei except the odd-odd, the modified GLDM showed relatively the best figures of merit for the odd-odd and superheavy nuclides.