Structural and decay properties of nuclei appearing in the $\alpha$-decay chains of $^{296,298,300,302,304}$120 within the relativistic mean-field formalism

An extensive study of $\alpha$-decay half-lives for various decay chains of isotopes of $Z$ = 120 is performed within the axially deformed relativistic mean-field (RMF) formalism by employing the NL3, NL3$^*$, and DD-ME2 parameter set. The structural properties of the nuclei appearing in the decay chains are explored. The binding energy, quadrupole deformation parameter, root-mean-square charge radius, and pairing energy are calculated for the even-even isotopes of $Z$ = 100 $-$ 120, which are produced in five different $\alpha$-decay chains, namely, $^{296}$120 $\rightarrow$ $^{260}$No, $^{298}$120 $\rightarrow$ $^{262}$No, $^{300}$120 $\rightarrow$ $^{264}$No, $^{302}$120 $\rightarrow$ $^{266}$No, and $^{304}$120 $\rightarrow$ $^{268}$No. A superdeformed prolate ground state is observed for the heavier nuclei, and gradually the deformation decreases towards the lighter nuclei in the considered decay chains. The RMF results are compared with various theoretical predictions and experimental data. The $\alpha$-decay energies are calculated for each decay chain. To determine the relative numerical dependency of the half-life for a specific $\alpha$-decay energy, the decay half-lives are calculated using four different formulas, namely, Viola-Seaborg, Alex-Brown, Parkhomenko-Sobiczewski, and Royer for the above said five $\alpha$-decay chain. We notice a firm dependency of the half-life on the $\alpha$-decay formula in terms of $Q_{\alpha}$-values for all decay chains. Further, the present study also strengthens the prediction for the island of stability in terms of magic number at the superheavy valley in the laboratories.