Empirical model for compound nucleus formation probability in heavy ion fusion reactions

Compound nucleus formation probability ( P_CN ) is very important to study the heavy ion fusion reactions forming superheavy nuclei. But we found only a few measurements performed as a function of energy till date utilizing eight heavy ion reactions. Accordingly, developing an empirical formula from the experimental data is difficult. However, one empirical formula is used to fit the experimental data, which is a function of projectile energy, fusion (Bass) barrier and three constants. These constants are different for different reactions and can only be known from experiment. Therefore, it cannot be used to predict these constants for any other reactions. To resolve this issue, we have developed a method to estimate these constants empirically as a function of beam energy, fusion barrier, Coulomb interaction parameter, and deformation parameter from five reactions and validated the model with other three reactions. Comparison of the present predictions with other models and experiments show that the present model is the best. We believe the proposed empirical formulae can be useful in the planning of the experiments for synthesizing the superheavy elements.