Three new behaviors have been found in comparisons of fusion cross sections for different collision systems. (1) Replacing the energy $E$ with a scaling one, $E_{\mathrm{scal}}=(E-V_g)/\left(\sqrt{2}{W}_g\right)$, is successful for washing out the Coulomb interaction in the spectra of fusion cross sections, where $V_g$ and $W_g$ are barrier height and width of the single-Gaussian barrier distribution model. (2) In a representation of $\sigma E$ vs the scaling energy, $E_{\mathrm{scal}}$, all data sets display in parallel. The ratio for $\sigma E$ from any two fusion systems over the whole range is a constant value. That behavior is also studied in another representation, in which the data sets display as parallel horizontal lines for any heavy-ion fusion system. (3) The constant ratio value is the ratio of parameter products, $R_g^2{W}_g$, of the two systems; where $R_g$ is the barrier radius obtained in the single-Gaussian barrier distribution model. Moreover, when comparing neighboring collision systems at the same $E_{\mathrm{scal}}$, the ratio of $\sigma$ is near a constant value within a few percent over the whole range. Thus a quantitative comparison for the fusion enhancement for neighboring systems is developed. The present finding could be beneficial for predicting unmeasured fusion cross sections.

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