Universal function for heavy-ion fusion cross sections

A universal function for heavy-ion fusion cross sections, $Y=\sqrt{\ensuremath{\pi}}X\mathit{erfc}(\ensuremath{-}X)+exp(\ensuremath{-}{X}^{2})$ is proposed. By scaling both the cross section $\ensuremath{\sigma}(E)$ and the energy $E$, heavy-ion fusion cross section data are found to follow closely a universal function over the whole energy range. The scaling is developed from either a simple, empirical single-Gaussian barrier distribution model for the representation ${d}^{2}(\ensuremath{\sigma}E)/d{E}^{2}$, or the modified Siwek-Wilczynski model. The cross section expressions of these models are analytical, and can be easily used for all heavy-ion fusion excitation functions. Thus a bench marking of heavy-ion fusion excitation functions has been achieved. A general discussion regarding the universal function is given.