Heavy cluster radioactivity and decay mode of Superheavy element 306^120

Background: Many theoretical studies and experimental attempts are conducted to synthesize SHN with Z =120 being an element with a proton magic number. The prediction of the island of stability also encourages scientists to search for the existence of super heavy nuclei near Z=120.Purpose: Main aim of our work is to predict all heavy cluster emissions from superheavy nuclei (SHN) 306120. Methods: Modified Generalized Liquid drop model (MGLDM) with Q value dependent pre-formation factor [Phys. Rev. C, 99, 064604 (2019)] is the theoretical model used to calculate the alpha and cluster decay half-life of SHN 306120. The spontaneous fission half-life is predicted using the shell effect and mass inertia dependent formula by our group [Phys. Rev. C, 104, 024617 (2021)].Results: We investigate all cluster emissions from 306120, and the fragment combination 123Cd (Z=48) leading to 183Hf daughter nucleus is predicted to be a probable heavy cluster decay with halflives comparable with alpha decay half-lives. The heavy cluster 137Xe (N=83) with 169Dy daughter nucleus is predicted to be the most probable cluster decay with the least half-life among all fragment combinations. Thus, our study shows the role of the magic number of proton and neutron in cluster decay. We also predict that the superheavy element 306120 decays by 4 alpha chains followed by spontaneous fission.Conclusions: The predicted half-life in the case of alpha decay and heavy cluster emission from SHN 306120 are within experimental limits and we hope that our predictions will guide future experiments.