Coulomb interaction dependence of optimal energy to synthesize superheavy elements

The production of superheavy elements beyond Z = 118 remains unattained through both cold and hot fusion techniques, primarily due to inadequate fusion reaction optimization involving projectile–target combinations and energy. Past efforts employed various theories to optimize these combinations. In our current study, we have successfully identified optimal fusion energies for synthesizing superheavy elements, employing an advance statistical model and dinuclear system models. The establishment of optimal energy governing rule is achieved through a comprehensive examination of the Coulomb interaction parameter, enabling precise determination of the optimal energy for successful fusion reactions in synthesizing superheavy elements. The confidence level of predicting optimal energies using the present formula varies between 97% to 99%. The predicted optimal energy using the present formula for five fusion reactions such as 208 Pb( 50 Ti,1n) 257 Rf, 208 Pb( 50 Ti,2n) 256 Rf, 209 Bi( 50 Ti,1n) 258 Db, 208 Pb( 58 Fe,1n) 265 Hs, and 244 Pu( 48 Ca,4n) 288 Fl were studied and are in good agreement with each other. Furthermore, we predicted the Optimal energies for fusion reactions leading to synthesize the superheavy element Z = 119 and 120. The presented empirical rule will certainly bring a revolution in the synthesis of superheavy elements. • Our study advances the synthesis of superheavy elements ( Z > 118 ) by identifying optimal fusion energies through a sophisticated statistical model and dinuclear system models. • This novel approach focuses on optimizing projectile–target combinations and energies, crucial for successful fusion reactions. • We establish an optimal energy rule by thoroughly examining the Coulomb interaction parameter, achieving a 97% to 99% confidence level in predicting these energies. • Our predictions for five reactions, including 208 Pb( 50 Ti, 1n) 257 Rf, 208 Pb(50Ti,2n) 256 Rf, 209 Bi( 50 Ti, 1n) 258 Db, 208 Pb( 58 Fe, 1n) 265 Hs, and 244 Pu( 48 Ca, 4n) 288 Fl, align well with experimental data. • Additionally, we forecast optimal energies for synthesizing elements Z = 119 and Z = 120. This empirical rule promises to revolutionize superheavy element synthesis by significantly improving fusion reaction optimization.