A universal function for heavy-ion fusion cross sections, $Y=\sqrt{\pi }X\mathit{erfc}(-X)+exp(-X^2)$ is proposed. By scaling both the cross section $\sigma \left(E\right)$ 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 $d^2\left(\sigma E\right)/d{E}^2$, 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.

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• Low & intermediate energy heavy-ion reactions
• Models & methods for nuclear reactions
• Nuclear fusion
• Nuclear reactions