Exploring the ground state bulk and decay properties of the nuclei in superheavy island

The $\alpha$-decay half-lives of 204 superheavy nuclei covering the range $114 \leq Z \leq 126$ have been investigated using the relativistic mean-field model (RMF) for NL3$^*$ parameter set. The ground state bulk properties such as binding energy, quadrupole deformation parameter ($\beta_2$ ), and root-mean-square charge radii for these nuclei are analyzed. Four different semi-empirical formulae, namely, the universal decay law (UDL), the Viola-Seaborg (VSS) formula, the modified universal decay law (MUDL), and the modified Brown formula (MBrown), are used to obtain the $\alpha$-decay half-lives for the considered nuclei. To examine the applicability of relativistic mean-field model within NL3$^*$ parametrization, the $\alpha$-decay energies, and the half-lives of a few known superheavy nuclei within the range 102 $\leq$ Z $\leq$ 118 are calculated and the results are compared with the experimental data along with the theoretical predictions. The $\alpha$-decay energies ($Q$-values) are estimated from the binding energies of the parent, and daughter from the RMF (NL3$^*$) parameter set. The calculated results are compared with macroscopic-microscopic Finite-Range-Droplet-Model (FRDM), Global Nuclear Mass Model (WS3, WS4), Weizsacker-Skyrme mass model (WS$^*$) predictions, and the experimental data, wherever available. The possible standard deviations are also estimated for experimental and various theoretical predictions. We find a good consistency for the experimental-to-UDL, FRDM-to-UDL, and WS4-to-UDL estimates of the decay energy and corresponding half-life. The present analysis provides the theoretical predictions within the microscopic model for the upcoming experiments on the superheavy region.