$\alpha$-decay systematics for superheavy nucleus: the effect of deformation of daughter nucleus

Recently, V.Yu. Denisov proposed a new empirical formula incorporating the deformation of the daughter nucleus, which has significantly improved the description of $\alpha$-decay half-lives for even-even nuclei compared to formulas neglecting the deformation of the daughter nucleus. In this work, we generalize the deformation of the daughter nucleus proposed by V.Yu. Denisov to the DUR model, the AKRA model, the New Geiger-Nuttall law, generating three improved versions of these models. We then employ both the original and modified the DUR model, the AKRA model, and the New Geiger-Nuttall law to investigate the $\alpha$-decay half-lives of 400 isotopes. Results show that among the six models, the modified AKRA model provides the closest agreement with experimental $\alpha$-decay half-life data. For comparative analysis, we use the new empirical formulas developed for the DUR model (DUR+D), the AKRA model (AKRA+D) and a new empirical (ND) proposed by V.Yu. Denisov to predict the $\alpha$-decay properties of 71 even-even nuclei with Z = 118, 120, 122, and 124. The predictions from the DUR+D model, the AKRA+D model, and ND are largely consistent overall. Notably, when the neutron number $N>190$, the predictions from the DUR+D model and the AKRA+D model exceed those of ND, which may be attributed to additional physical contributions (e.g., the hexadecapole and the hexacontatetrapole deformation of the deformed daughter nucleus) incorporated in the DUR+D model and the AKRA+D model but not in ND.