Predictions for the synthesis of the Z=120 superheavy element

The possible stable and radioactive beam-induced hot fusion reactions for the production of new superheavy element (SHE) $Z=120$ are investigated within the dinuclear system model. Our investigation shows that the reaction $^{45}\mathrm{Sc}+^{252}\mathrm{Es}$ has a relatively large evaporation residue cross-section (ERCS) for the synthesis of SHE $Z=120$ due to its slightly larger mass asymmetry. In addition, we analyzed the effects of fission barrier and neutron separation energy of superheavy nuclei on ERCS. To synthesize the double-magic $Z=120$ and $N=184$ nucleus predicted by the relativistic mean-field model, some radioactive beam-induced fusion reactions, which can be performed in available experimental equipment, for producing superheavy nucleus $^{304}120$ in neutron evaporation channels are investigated systematically. We find that the hot fusion reaction $^{50}\mathrm{Ca}+^{257}\mathrm{Fm}$ in the $3n$ evaporation channel is optimal for synthesizing the superheavy nucleus $^{304}120$. We hope these predictions will shed new light timely for the recent experiments on the synthesis of $Z=120$ superheavy element and the search for superheavy stability islands.