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 ²⁰⁸Pb(⁵⁰Ti,1n)²⁵⁷Rf, ²⁰⁸Pb(⁵⁰Ti,2n)²⁵⁶Rf, ²⁰⁹Bi(⁵⁰Ti,1n)²⁵⁸Db, ²⁰⁸Pb(⁵⁸Fe,1n)²⁶⁵Hs, and ²⁴⁴Pu(⁴⁸Ca,4n)²⁸⁸Fl 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.