Systematics of Coulomb barriers deduced from experimental capture cross sections and then used to predict the capture cross sections

Abstract

The experimental data of capture cross sections for 220 light, medium and heavy reaction systems for formation 45≤Z≤102 compound nucleus have been analyzed using a simple formula, this formula is derived by assuming the Gaussian shape of the barrier distribution function. For each reaction, the empirical values of the barrier height, barrier radius and width of the barrier distribution were determined by fitting the experimental data. The obtained mean values of the barrier height have been used for determination of the parameters of the analytical expression in the barrier heights. One finds that the mean barrier heights calculated with analytical expression are reproduced with an accuracy of about 2 MeV. However, other frequently used potentials are systematically overestimated the empirical values, especially for heavy systems. Using analytical expression in the barrier heights can predict nicely the capture cross sections for formation superheavy nuclei at above as well as below barrier energies.