Rotational effect on $α$-particle radioactivity of even-even $^{254,256}$Rf isotopes using various semi-empirical formulae: Rotational effect on $α$-particle radioactivity of even-even $^{254,256}$Rf nuclei (Письма в ЭЧАЯ, 2024)
The present work cover the theoretical investigation of the $α$-decay half-lives of the {\it even-even} $^{254,256}$Rf chains using the relativistic mean field (RMF) formalism using the PC-PK1 parameter set. The effect of rotation on the stability of these neutron-deficient nuclei is appraised. Six different semi-empirical formulae, namely, the Viola-Seaborg semi-empirical formula, Modified Brown formula, Semiempirical formula based on fission theory, Royer Formula, Wang Formula, and Modified Yibin {\it et al.} formula are adopted for the estimation of decay half-live for the considered chain. The predictive accuracy of each of these formulae is evaluated by comparing them to the experimental data. The decay energies ($Q_α$) for the alpha decay chain are calculated from The present calculation revealing that the relative dependency of the employed formulae is hinged on their respective constituents. We observed that the binding energy obtained with the rotational effect improves the decay half-life for all semi-empirical formulae in terms of $Q$-values. This can be correlated with the distinct consideration of parameter $S$, which incorporates the shell effect. Thus, for deformed parents, the rotational effect is required to obtain reasonable decay properties and systematic investigation will be performed in the subsequent study.