Abstract
The predictions on the $\ensuremath{\alpha}$-decay chains of the isotopes of the superheavy nuclei with $Z=120$ in the range $272\ensuremath{\le}A\ensuremath{\le}319$ have been done within the Coulomb and proximity potential model for deformed nuclei. A comparison of our calculated $\ensuremath{\alpha}$ half-lives with the values computed using the Viola-Seaborg [J. Inorg. Nucl. Chem. 28, 741 (1966)] systematic, the universal curve of Poenaru et al. [Phys. Rev. C 74, 014312 (2006)], and the analytical formulas of Royer [J. Phys. G: Nucl. Part. Phys. 26, 1149 (2000)] show good agreement with each other. An extensive study on the spontaneous fission half-lives of all the isotopes under study has been performed to identify the mode of decay of these isotopes. The study reveals that the $\ensuremath{\alpha}$-decay half-lives and the mode of decay of the isotopes of $^{298,299}120$, which are evaluated by using our formalisms, agree well with the experimental observations of Oganessian et al. [Phys. Rev. C 79, 024603 (2009)]. Our study on the isotopes of $Z=120$ predicts that the $\ensuremath{\alpha}$ decay restricts within the range $277\ensuremath{\le}A\ensuremath{\le}308$ as those isotopes with $A\ensuremath{\le}276$ and those nuclei with $A \ensuremath{\ge}$ 309 do not survive fission. We have also forecasted the mode of decay of $^{288\ensuremath{-}302}120$ superheavy nuclei as six consistent $\ensuremath{\alpha}$ chains from the nuclei of $^{288,289,291\ensuremath{-}295}120$, seven consistent $\ensuremath{\alpha}$ chains from the nuclei of $^{290}120$, five consistent $\ensuremath{\alpha}$ chains from the nuclei of $^{296,297}120$, and three consistent $\ensuremath{\alpha}$ chains from the nuclei of $^{300\ensuremath{-}302}120$, which could be of great interest to the experimentalists. The one-proton and two-proton separation energy calculations on $^{272\ensuremath{-}319}120$ superheavy nuclei have revealed that the isotopes spanning the range $273\ensuremath{\le}A\ensuremath{\le}291$ may be considered to be the probable proton emitters.
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