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It is shown that the pairing correlation is very important for the two-neutron transfer reactions, for reaction induced by 84 MeV 18O on several targets with low collectivity in its ground state (spherical), proceeding through the one-step process (concerning to transfer process). For the transition to lower excited states, the one-step process also dominated, for the final nuclei having also low collectivity. On the contrary, if the collectivity of these states is considerable, the two-neutron transfer reaction is dominated by a two-step process through an intermediate partition. We present our results for 12,13C(18O,16O) 12,13C[1,2], 16O(18O,16O) 18O[3,4], 64Ni(18O,16O)66Ni[5] and 28Si(18O,16O)30Si[6] by analysing the two-neutron transfer angular distributions. We compare our results with similar results for the 206Pb(18O,16O)208Pb[7] and 7Be(9Be,7Be)9Be[8] reactions, and with the analysis of the quasi-elastic barrier distributions for the 63Cu +18O system [9]. We also show the evidences recently found for the observations of Giant Pairing Vibrations in the 12,13C(18O,16O) 12,13C reactions [10]. Some preliminary results of the effect of pairing correlations in two-protons transfer reactions are also shown. Our ability to describe microscopically multi-nucleon transfer reactions that compete with the double-charge exchange reactions within the NUMEN project [11] will be also discussed.
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