Systematic Study Of Fusion Barrier For Heavy-ion Fusion Reactions

Heavy-ion fusion reactions are essential for the synthesis of super-heavy nuclides.Studying the Coulomb barrier and near-barrier nuclear reactions can help us understand the interaction of atomic nuclei and reveal the essence of nuclear force,which is crucial for exploring the synthesis of super-heavy nuclei,the fusion reaction of heavy ions under very deep barriers,and the properties of nuclear structure.Using the time-dependent Hartree-Fock(TDHF)theory and experimental fusion excitation functions,we analyzed the relationship between the barrier radius and energy.The results reveal that due to dynamic effects in the reactions,the barrier radius shows a trend of strengthening at near-barrier and sub-barrier energies.Based on the multi-dimensional barrier penetration model,we considered the energy dependence of the barrier radius in heavy-ion fusion reactions and proposed an empirical expression to describe the energy dependence of the barrier radius,thereby improving the SW fusion cross section formula.The modified SW(MSW)formula better reproduces the experimental fusion excitation functions and provides a refined structure of the barrier distribution.Based on 443 groups of measured cross sections from 367 reaction systems,we used the MSW formula to systematically extract information about the fusion barrier parameters,and proposed the parametric empirical formulas of barrier height,distribution width and barrier radius.We found that the fusion excitation functions for approximately 60%of reaction systems can be more accurately described using the MSW formula.Considering both the influence of the geometry radii and that of the reduced de Broglie wavelength of the colliding nuclei,the barrier heights are well reproduced with only one model parameter.In addition,we compared the deviation of the extracted barrier heights with the calculated values from various theoretical models.We found that the MSW potential and BW91 potential based on a Woods-Saxon form produced comparatively better results.Finally,We conducted a preliminary discussion of reaction types in different mass regions,analyzing the competition between evaporation fusion,fusion-fission,and quasifission reactions during the evolution of the composite system.We propose that the ratio of fission barrier to excitation energy can serve as a quantitative ’probe’ for monitoring whether composite nuclei undergo fission.Additionally,the height of the quasi-fission barrier can be used to estimate the probability of quasi-fission.