Predicted cross sections for the synthesis of $Z=120$ fusion via ${}_{54}\mathrm{Cr}+{}_{248}\mathrm{Cm}$ and ${}_{50}\mathrm{Ti}+{}_{249}\mathrm{Cf}$ target-projectile combinations

The production of superheavy elements (SHE) is confronted with significant experimental difficulties owing to extremely low cross sections for their formation in heavy-ion fusion reactions. Accurate predictions of these cross sections along with the corresponding excitation functions are of the utmost importance for future experiments. Theoretical studies are needed in order to investigate the decay properties of excited SHE. A recent conclusion on the importance of the neck-length parameter [S. Chopra, N. Goel, M. K. Sharma, P. O. Hess, and Hemdeep, Phys. Rev. C 106, L031601 (2022)] within the framework of the dynamical cluster-decay model (DCM) became foundational for this work, which explained the ability of the DCM to predict the decay cross sections in hot fusion reactions. The model is a nonstatistical description for the decay of a compound nucleus (CN). The only parameter of the model is the neck-length parameter, which is related to the total kinetic energy $\mathrm{TKE}\left(T\right)$ or the effective $Q$ value $Q_{\mathrm{eff}}(T$) at the temperature $T$ of the CN. This work shows that the hot fusion reactions ${}_{54}\mathrm{Cr}+{}_{248}\mathrm{Cm}$ and ${}_{50}\mathrm{Ti}+{}_{249}\mathrm{Cf}$, in the decay of $4n$ evaporation channel may be more favorable for the synthesis of the $Z=120$ SHE. After the emission of four neutrons, ${}_{302}120_{*}$ can reach ${}_{298}120$ and this would lead to the formation of ${}_{294}118$ after one $\alpha$ decay. In the same way, ${}_{50}\mathrm{Ti}+{}_{249}\mathrm{Cf}$ can end up at some known nuclei. If this happens, it would be a positive sign for the synthesis of $Z=120$ from one of these two nuclear reactions. The present work calculated the cross sections of all possible decay modes, i.e., evaporation residues, fission, and quasifission for the chosen reactions. In addition, an evaluation for the total or capture cross section is applied, for the case of $Z=120$, without the use of any input of a single experimental data. These predictions may be useful for upcoming experiments.