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The present work is a theoretical study on the $\alpha$-decay half-lives of the even-even $^{254,256}$Rf isotopic chains using six different semi-empirical formulae, namely, the Viola-Seaborg semi-empirical formula (VSS), Modified Brown formula (mB1), Semiempirical formula based on fission theory (SemF IS2), Royer Formula (R), Wang Formula (wang), and Modified YQZR formula (MYQZR)[1]. The predictive accuracy of each of these formulae is evaluated by comparing them to the experimental data[2]. The decay energies ($Q_\alpha$) for the alpha decay chain are calculated from the relativistic mean field (RMF) formalism [3] using the PC-PK1 parameter set [4]. Furthermore, the effect of rotation on the stability of these neutron-deficient nuclei is separately appraised. Our calculation reveals that the relative dependency of the employed formulae is hinged on their constituents. Thus, the modified YQZR formula of $\alpha$-decay half-lives gives a closer agreement with the experimental measurement due to its inclusion of the asymmetry terms. The relevance of this study in the superheavy region to astrophysics is concisely discussed.
[1]. D. T.Akrawy, D. N.Poenaru, A. H. Ahmed, L.Sihver, Nucl. Phys. A 1021, 122419 (2022). https://doi.org/10.1016/j.nuclphysa.2022.122419
[2]. F.G. Kondev, M. Wang, W. J. Huang, S.Naimiand G. Audi, Chin. Phys. C 45 030001 (2021).https://doi.org/10.1088/1674-1137/abddae
[3]. J. T. Majekodunmi, M. Bhuyan, D. Jain, K. Anwar, N. Abdullah, and Raj Kumar, Phys. Rev. C 105, 044617 (2022). https://doi.org/10.1103/PhysRevC.105.044617
[4]. K. Y. Zhang et al., Atom. Data. Nucl. Data Tabl. 144, 101488 (2022). https://doi.org/10.1016/j.adt.2022.101488
