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Double charge exchange (DCE) reactions could provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-β decay. To achieve this goal, a detailed description of the reaction mechanism is mandatory. This requires the full characterization of the initial and final-state interactions, which are poorly known for many of the projectile-target systems involved in future DCE studies. Among these, we intend to study the 20Ne + 130Te and 18O + 116Sn systems at 15.3 AMeV, which are particularly relevant due to their connection with the 130Te→130Xe and 116Cd→116Sn double-β decays. We measure the elastic and inelastic scattering cross-section angular distributions and compare them with theoretical calculations performed in the optical model, one-step distorted wave Born approximation, and coupled-channel approaches using the São Paulo double-folding optical potential. A good description of the experimental data in the whole explored range of transferred momenta is obtained provided that couplings with the 21+ states of the projectile and target are explicitly included within the coupled-channel approach. These results are relevant also in the analysis of other quasi-elastic reaction channels in these systems, in which the same couplings should be included.

International audience; The article describes the main achievements of the NUMEN project together with an updated and detailed overview of the related R&D activities and theoretical developments. NUMEN proposes an innovative technique to access the nuclear matrix elements entering the expression of the lifetime of the double beta decay by cross section measurements of heavy-ion induced Double Charge Exchange (DCE) reactions. Despite the fact that the two processes, namely neutrinoless double beta decay and DCE reactions, are triggered by the weak and strong interaction respectively, important analogies are suggested. The basic point is the coincidence of the initial and final state many-body wave functions in the two types of processes and the formal similarity of the transition operators. First experimental results obtained at the INFN-LNS laboratory for the$^{40}$Ca($^{18}$O,$^{18}$Ne)$^{40}$Ar reaction at 270MeV give an encouraging indication on the capability of the proposed technique to access relevant quantitative information. The main experimental tools for this project are the K800 Superconducting Cyclotron and MAGNEX spectrometer. The former is used for the acceleration of the required high resolution and low emittance heavy-ion beams and the latter is the large acceptance magnetic spectrometer for the detection of the ejectiles. The use of the high-order trajectory reconstruction technique, implemented in MAGNEX, allows to reach the experimental resolution and sensitivity required for the accurate measurement of the DCE cross sections at forward angles. However, the tiny values of such cross sections and the resolution requirements demand beam intensities much larger than those manageable with the present facility. The on-going upgrade of the INFN-LNS facilities in this perspective is part of the NUMEN project and will be discussed in the article.