Theoretical predictions on cluster radioactivity of superheavy nuclei with Z=119, 120

In this work we investigate cluster radioactivity (CR) of new superheavy elements with $Z=119$ and 120 based on two successful theoretical methods with modified parameters, the density-dependent cluster model (DDCM) and the unified decay formula (UDF). Firstly we employ the DDCM and UDF to accurately reproduce the experimental half-lives of cluster emissions, which demonstrates high reliability of our theoretical methods. Then we systematically predict probable cluster modes of $^{293-311}$119 and $^{293-302}$120 as well as their corresponding decay energies and half-lives. The half-lives of cluster decay derived from DDCM are consistent with those from UDF. As a result, our results reveal that the cluster emission of $^{8}$Be, emitted from the $Z=$119 and 120 isotopic chains, exhibits the minimum half-life for cluster emission, thereby $^{8}$Be emission is considered as the most probable cluster decay mode. Moreover, we explore the competition between $\alpha$ decay and CR and find that $\alpha$ decay may be the dominant decay mode against CR. Furthermore, a good linear relationship between the decay energy and the number of $\alpha$ particles within the emitted cluster is extended to range of superheavy nuclei (SHN). We anticipate that our theoretical predictions for CR will provide valuable references for the experimental synthesis of new SHN.