In our recent studies,an empirical barrier distribution was proposed for a unified description of the fusion cross sections of light and medium-heavy fusion systems,the capture cross sections of the reactions leading to superheavy nuclei,and the large-angle quasi-elastic scattering cross sections based on the Skyrme energy-density functional approach.In this paper,we first give a brief review of these results.Then,by examining the barrier distributions in detail,we find that the fusion cross sections depend more strongly on the shape of the left side of the barrier distribution while the quasi-elastic scattering cross sections depend more strongly on the right side.Furthermore,by combining these studies and the HIVAP calculations for the survival probability,the formation probability of the compound nucleus is deduced from the measured evaporation residue cross sections for “cold” and “hot” fusion reactions. In our recent studies, an empirical barrier distribution was proposed for a unified description of the fusion cross sections of light and medium-heavy fusion systems, the capture cross sections of the reactions leading to superheavy nuclei, and the large-angle quasi-elastic scattering cross sections based on the Skyrme energy-density functional approach. In this paper, we first give a brief review of these results. Chen, by examining the barrier distributions in detail, we find that the fusion cross sections depend more strongly on the shape of the left side of the barrier distribution while the quasi-elastic scattering cross sections depend more strongly on the right side. Furthermore, by combining these studies and the HIVAP calculations for the survival probability, the formation probability of the compound nucleus is deduced from the measured evaporation residue cross sections for “cold ” and “hot ” fusion reactions.