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An extensive study of $\alpha$-decay half-lives for various decay chains ofisotopes of $Z$ = 120 is performed within the axially deformed relativisticmean-field (RMF) formalism by employing the NL3, NL3$^*$, and DD-ME2 parameterset. The structural properties of the nuclei appearing in the decay chains areexplored. The binding energy, quadrupole deformation parameter,root-mean-square charge radius, and pairing energy are calculated for theeven-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, andgradually the deformation decreases towards the lighter nuclei in theconsidered decay chains. The RMF results are compared with various theoreticalpredictions and experimental data. The $\alpha$-decay energies are calculatedfor each decay chain. To determine the relative numerical dependency of thehalf-life for a specific $\alpha$-decay energy, the decay half-lives arecalculated using four different formulas, namely, Viola-Seaborg, Alex-Brown,Parkhomenko-Sobiczewski, and Royer for the above said five $\alpha$-decaychain. We notice a firm dependency of the half-life on the $\alpha$-decayformula in terms of $Q_{\alpha}$-values for all decay chains. Further, thepresent study also strengthens the prediction for the island of stability interms of magic number at the superheavy valley in the laboratories.

modern physics letters a

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