Dynamic Effects of Breakup on Fusion Reactions of Weakly Bound Nuclei

In the last years an important question has been asked and not yet fully answered [1]: How does the low breakup threshold of a halo nucleus influence their fusion cross sections? One can distinguish effects of two kinds. First, there are the static effects associated with the longer tail of the nuclear density, arising from the halo nucleons. This tail gives rise to a more diffuse potential, with a lower barrier. This effect enhances the fusion cross section. The second kind are the dynamical effects associated with the strong coupling between the elastic and the breakup channels. The consequences of this coupling are more difficult to assess. It may hinder the fusion process by removing from the incident channel some flux that would otherwise contribute to fusion. On the other hand, it may lead to a lower eigen-barrier, as in the case of coupling to a bound channel, and thus enhance the fusion cross section. In order to investigate the role of weak binding in the fusion process, on can follow two procedures. First, on can compare fusion cross sections with predictions of theoretical models. For this purpose it is necessary to have a reliable bare potential, obtained through a systematic procedure. The natural choice is to use a folding potential based on realistic densities. However, this procedure is restricted to a single system. Therefore, it does not allow the comparison of results for different collision partners. The second possibility is to compare the fusion cross section with the corresponding results for a strongly bound isotope with the same target. In this case, it is necessary to reduce the data in order to eliminate trivial differences arising from the system size. In the present contribution, we discuss the reduction techniques available in the literature, we show their shortcomings [2,3] and we propose a new method for comparing fusion data for different systems [2,3]. This method can be applied both above and below the Coulomb barrier. The method consists of introducing a universal fusion function (UFF), to which the data for any system should be compared. The dynamical effects of low breakup threshold can then be assessed through this comparison. We show that the effects of breakup coupling can be singled out through an appropriate re-normalization of the fusion cross section. The experimental fusion cross section is divided by a theoretical cross section, calculated by the coupled-channel method, including couplings to all relevant bound channels. We apply this method to the available fusion data for weakly bound projectiles (stable, neutron halo and proton halo) and arrive at systematic conclusions about the problem [3,4]. We also extend this formalism to analyze total reaction cross sections of weakly bound systems and the contribution of the breakup process to them, in wide target mass and energy ranges.(author)