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Systematic study on probable projectile-target combinations for the synthesis of the $^{302}$120 superheavy nucleus

Probable projectile-target combinations for the synthesis of superheavy element $^{302}$120 have been studied taking Coulomb and proximity potential as the interaction barrier. The probabilities of compound nucleus formation, PCN for the projectile-target combinations found in the cold reaction valley of $^{302}$120 are estimated. At energies near and above the Coulomb barrier, we have calculated the capture, fusion and evaporation residue cross sections for the reactions of all the probable projectile-target combinations so as to predict the most promising projectile-target combinations for the synthesis of SHE $^{302}$120 in heavy ion fusion reactions. The calculated fusion and evaporation cross section for the more asymmetric (hotter) projectile-target combination is found to be higher than the less asymmetric (colder) combination. It can be seen from the nature of quasi-fission barrier height, mass asymmetry, probability of compound nucleus formation, survival probability and excitation energy, the systems $^{44}$Ar + $^{258}$No, $^{46}$Ar + $^{256}$No, $^{48}$Ca + $^{254}$Fm, $^{50}$Ca + $^{252}$Fm, $^{54}$Ti + $^{248}$Cf, $^{58}$Cr + $^{244}$Cm in the deep region I of cold reaction valley, and the systems $^{62}$Fe + $^{240}$Pu, $^{64}$Fe + $^{238}$Pu, $^{68}$Ni + $^{234}$U, $^{70}$Ni + $^{232}$U, $^{72}$Ni + $^{230}$U, $^{74}$Zn + $^{228}$Th in the other cold valleys are identified as the better projectile-target combinations for the synthesis of $^{302}$120. Our prediction on the synthesis of $^{302}$120 superheavy nuclei using the combinations $^{54}$Cr+$^{248}$Cm, $^{58}$Fe+$^{244}$Pu, $^{64}$Ni+$^{238}$U and $^{50}$Ti+$^{249}$Cf are compared with available experimental data and other theoretical predictions.