Heavy-ion fusion cross-sections predicted by a phenomenological formula

Modeling Heavy-Ion Fusion Cross Section Data via a Novel Artificial Intelligence Approach

“…As evident, the neuro-genetic algorithm achieves (Lower panel) As in the upper panel, but here the predictions are obtained with the phenomenological formula discussed in Ref. [31].…”

“…In Fig. 4, we compare our results, for some light systems, with the prediction of a phenomenological approach adopted to describe fusion data [31], previously published in the literature. This model is derived starting from the modified sum-of-difference method (MSOD), and it can also reasonably reproduce some details in proximity of the maxima of fusion excitation functions.…”

“…As an example, in Refs. [31,16,28,30,29] are reproduced in a satisfactory way complete fusion data from several collision systems in the I-II regions, while in Ref. [15] the description of data is limited to region III, where complete fusion is in competition with different reaction mechanisms [32].…”

“…This fact is not surprising, considering that the fusion process is intimately linked to Coulomb barrier. Side effects of the Coulomb related term Z 1 Z 2 on the fusion cross section in heavy systems were pointed out, for example, by Vaz et al [50], while it is worth noting that several other phenomenological approaches show a clear dependence on Z 1 Z 2 (e.g., [31,16,29,30]). Besides the very weak, logarithmic, dependence on the target two-neutron separation energy present in the higher complexity model, no significant correlations on other features related to nuclear structure properties, or even mass asymmetries, can be evidenced with this approach.…”

“…Such approaches are useful to make numerical evaluations on fusion cross sections but have some limitations: they often describe just a limited part of the energy regimes where fusion can occur, or they are lacking physical boundaries. For example, a phenomenological approach to fusion should guarantee that the fusion cross section goes toward zero at very low bombarding energies (deep sub-barrier regime) and at very high energies (where incomplete fusion and vaporization would be dominant in central reaction events), but the continuous evolution of the reaction mechanisms as a function of energy and the impact of quantum effects (such as tunnelling through barriers at low energies) make it difficult to fulfill these requirements (see, e.g, [31,33,16]).…”