Reproducing heavy-ion fusion cross sections at extreme sub-barrier energies with a simple formula: Analysis of fusion hindrance with a Gaussian barrier distribution

.Heavy-ion fusion hindrance occurs at extreme sub-barrier energies. This behavior is well reproduced with a simple cross section formula, which was developed by Siwek-Wilczynska et al., based on a single-Gaussian distribution of fusion barrier heights, before the discovery of the hindrance phenomenon. This expression has not yet been widely used and referenced in the literature. An analysis by using this simple formula is presented for 29 systems, from O-16 + O-18 to Ni-64 + Sn-124 , all being measured down to less than 10b. The agreement with the data is even better than the ones from sophisticated Coupled-channels calculations. This simple expression also applies to fusion reactions in lighter systems. The three parameters contained in this formula vary in a relatively smooth fashion over the whole mass range, and can be used to extrapolate cross sections or to obtain an estimate of the excitation function for systems which have not been measured. Extensions and restrictions of this method are also discussed.