Comparative study of α-decay half-lives for Au, Hg, and Tl isotopes using the MGLDM, empirical formulae, and NpNn-based preformation probabilities

The alpha decay half-lives of Au, Hg, and Tl isotopes in the mass number range 168–198 have been investigated using the Modified Generalized Liquid Drop Model (MGLDM). In addition, we calculated the half-lives using ten different empirical formulae. The dependability of various methods is analyzed by comparing the predicted half-lives with experimental values. The MGLDM with preformation factor gives the standard deviation of 0.5923, and Modified Empirical Royer Formula (MERF) gives a value of 0.5734, which are the lowest values among model predictions and empirical formulae calculations, respectively. The New Geiger-Nuttal plot, which accommodates both favoured and unfavoured alpha transitions on a single linear curve, enhances the valuability of our model. The linear trends of the logarithmic preformation factors with the combinations of valence nucleons, shell closures, and isospin asymmetry are analysed, and this study reflects the shell effects of nuclear structure. The calculated half-lives using \({N}_{p}{N}_{n}\) scheme in the framework of MGLDM are comparable with the experimental results with a small value of standard deviation.