Improved unified formulas for α-decay and cluster radioactivity in heavy and superheavy nuclei: effects of daughter-nucleus deformation

Enhanced unified empirical formulas for both α α - and cluster decay half-lives have been developed by incorporating the effects of angular momentum, isospin asymmetry, and, most importantly, the deformation of daughter nuclei. The updated coefficients were determined using the latest experimental data for α α -decay half-lives of 573 nuclei in the range $$52< Z < 118$$ 52 < Z < 118 , together with 21 available cluster decay half-lives. To model the impact of deformation, two additional terms – dependent on the quadrupole and hexadecapole deformation parameters – were introduced. Our analysis shows that the quadrupole deformation parameter ( β ₂ β 2 ) significantly improves agreement with experiment, while the hexadecapole deformation parameter ( β ₄ β 4 ) produces only marginal effects. These revised empirical formulas yield predictions for both α α - and cluster decay half-lives that are in strong agreement with other similar calculations and have been validated through comparisons with recent experimental results and theoretical predictions. Furthermore, the new formulas were applied to estimate the half-lives of cluster emissions from superheavy nuclei with $$Z=120$$ Z = 120 , 122, 124, and 126, and the variation of log ₁₀ T_α log 10 T α with changes in neutron number was thoroughly explored.