Refinement of an analytical capture cross section formula

An analytical formula with high accuracy is proposed for a systematic description of the capture cross sections from light to superheavy reaction systems. Based on the empirical barrier distribution (EBD) method, three key input quantities are refined by introducing the Coulomb exchange term to the Coulomb parameter $z$ for calculating the barrier height, incorporating the $Q$-value into the barrier distribution width calculations, and considering the surface effects of light nuclei and the deep inelastic scattering effects of superheavy systems on the barrier radius. These refinements substantially improve the model accuracy, not only the accuracy of the barrier height but also the accruacy of the capture cross sections at energies around the Coulomb barrier. The mean value of the deviations (in logarithmic scale) between the predicted cross sections and the data for a total of 426 reaction systems with $ 35 < Z_1 Z_2 < 2600$ is sharply reduced from 3.485 to 0.166.