\begin{document}$ Z=119 $\end{document} and 120 based on two successful theoretical methods with modified parameters: the density-dependent cluster model (DDCM) and unified decay formula (UDF). First, we employ the DDCM and UDF to accurately reproduce the experimental half-lives of cluster emissions, which demonstrates the high reliability of our theoretical methods. Then, we systematically predict the probable cluster modes of 293-311119 and 293-302120 as well as their corresponding decay energies and half-lives. The half-lives of cluster decay derived from the DDCM are consistent with those from the UDF. Therefore, our results reveal that the cluster emission of 8Be, emitted from the \begin{document}$ Z= $\end{document}119 and 120 isotopic chains, exhibits the minimum half-life for cluster emission, and hence, 8Be emission is considered the most probable cluster decay mode. Moreover, we explore the competition between α decay and CR and find that α decay may be the dominant decay mode against CR. Furthermore, the good linear relationship between the decay energy and the number of α particles within the emitted cluster is extended to the range of superheavy nuclei (SHN). We anticipate that our theoretical predictions for CR will provide valuable references for the experimental synthesis of new SHN."> Theoretical predictions on cluster radioactivity of superheavy nuclei with <i>Z </i>= 119, 120 -
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