Universal Wong formula for capture cross sections from light to super-heavy systems

A universal Wong formula is proposed with refined model parameters for a systematic description of the capture cross sections for heavy-ion fusion reactions from C+C to Ni+U, in which the barrier parameters and the barrier distribution are determined by the entrance-channel nucleus-nucleus potential based on the Skyrme energy density functional. With introducing a constraint to the width of the barrier distribution and a pocket-depth dependent barrier radius, the capture excitation functions for a number of fusion reactions involving different nuclear structure effects are remarkably well reproduced, particularly for the reactions between light nuclei and those forming super-heavy nuclei. The systematic decreasing behavior of the geometric radii with the depth of capture pocket due to the influence of deep inelastic scattering is clearly observed in the TDHF calculations for super-heavy systems. The predicted capture cross sections for $^{54}$Cr + $^{238}$U at above barrier energies are evidently smaller than the corresponding results of more asymmetric projectile-target combination $^{50}$Ti + $^{242}$Pu due to the shallower capture pocket in Cr+U.