Refinement of an analytical capture cross section formula

Abstract

An analytical formula with high accuracy is proposed for a systematic description of the capture cross sections at near-barrier energies from light to superheavy reaction systems. Based on the empirical barrier distribution (EBD) method, three key input quantities are refined by introducing nuclear surface correction to the Coulomb parameter $z$ for calculating the barrier height, incorporating the reaction $Q$-value and shell correction into the barrier distribution width calculations, and considering the deep inelastic scattering effects of superheavy systems on the barrier radius. With these refinements, not only the accuracy of the calculated barrier height but also the accuracy of the predicted capture cross sections, is substantially improved. The average deviation (in logarithmic scale) between the predicted cross sections and the experimental data for a total of 426 reaction systems with $ 35 < Z_1 Z_2 < 2600$ is sharply reduced from 3.485 to 0.113.