Study of Rotational Effect on Even-Even ^254,256Rf Isotopes of α-Particle Radioactivity Using Various Semi-Empirical Formulae

Abstract

The present work covers the theoretical investigation of the $\alpha$-decay half-lives of the even-even $^{{254,256}}$Rf chains using deformed relativistic Hartree–Bogoliubov theory in the continuum (DRHBc) formalism with 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 et al. formula are adopted for the estimation of the decay half-lives of the considered chain. The predictive accuracy of each of these formulae is evaluated by comparing them to the experimental data. The calculation reveals 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. From the analysis of the Q-values and the calculated half-lives, the $^{{246,248}}$Fm isotopes with (Z = 100) display a unique feature that suggests the presence of shell stability and the peculiarity of the trans-fermium region is discussed. Thus, for deformed parents, the rotational effect is required to obtain reasonable decay properties and systematic investigation will be performed in the subsequent study.