Universal function for heavy-ion fusion cross sections

A universal function for heavy-ion fusion cross sections, Y=πXerfc(-X)+exp(-X2) is proposed. By scaling both the cross section σ(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 d2(σE)/dE2, 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.