Optimal incident energy of heavy ion fusion

We systematically explored all conceivable combinations of projectiles and targets through experimental studies, focusing on the synthesis of lanthanides to superheavy nuclei within the atomic number range of 58117. Utilizing the dinuclear system model, we evaluated evaporation residue cross sections for each fusion reaction, identified optimal energies associated with larger evaporation residue cross sections. Our study delved into the influence of entrance channel parameters such as mass asymmetry, charge asymmetry, charge product, Coulomb interaction parameter, mean fissility, and fusion barrier height on these optimal energies. Notably, a systematic variation in optimal energies was observed for the Coulomb interaction parameter. Additionally, the deformation parameter exhibited an influence on optimal energies, and pronounced discrepancies were noted in specific fusion reactions such as ^40Ar (^181Ta, 4n) ^217Pa, and for the reactions such as ^16O (^134Ba, 4n) ^146Gd, ^4He (^166Er, 3n) ^167Yb, and ^48Ca (^249Bk, 4n) ^293Ts, when compared to other fusion reactions explored. The empirical formula presented successfully replicates experimental optimal energies for the atomic number range 58117. Its straightforward application involves inputting the atomic and mass numbers of the projectile and target nuclei, along with deformation parameters, underscoring its simplicity and effectiveness in predicting optimal energies in diverse fusion reactions. This simplicity underscores the predictive power of the proposed formula, offering a valuable tool for understanding and predicting optimal energies in a wide range of fusion reactions involving lanthanides and superheavy nuclei.