Double charge exchange (DCE) reactions could provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-$\beta$ 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 ${}^{20}$Ne + ${}^{130}$Te and ${}^{18}$O + ${}^{116}$Sn systems at 15.3 AMeV, which are particularly relevant due to their connection with the ${}^{130}$Te${\to }^{130}$Xe and ${}^{116}$Cd${\to }^{116}$Sn double-$\beta$ 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 2${}_1^{+}$ 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.

Neutrinos are so far the most elusive known particles, and in the last decades many sophisticated experiments have been set up in order to clarify several questions about their intrinsic nature, in particular their masses, mass hierarchy, intrinsic nature of Majorana or Dirac particles. Evidence of the Neutrinoless Double-Beta Decay (NDBD) would prove that neutrinos are Majorana particles, thus improving the understanding of the universe itself. Besides the search for several large underground experiments for the direct experimental detection of NDBD, the NUMEN experiment proposes the investigation of a nuclear mechanism strongly linked to this decay: the Double Charge Exchange reactions (DCE). As such reactions share with the NDBD the same initial and final nuclear states, they could shed light on the determination of the Nuclear Matrix Elements (NMEs), which play a relevant role in the decay. The physics of DCE is described elsewhere in this issue, while the focus of this paper will be on the challenging experimental apparatus currently under construction in order to fulfil the requirements of the NUMEN experiment. The overall structure of the technological improvement to the cyclotron, along with the newly developed detection systems required for tracking and identifying the reaction products and their final excitation level are described.

Within the NUMEN project, we present experimental issues and data reduction for the ¹¹⁶Cd(²⁰Ne,²⁰F)¹¹⁶In single charge exchange, ¹¹⁶Cd(²⁰Ne,¹⁸O)¹¹⁸In two-proton transfer and ¹¹⁶Cd(²⁰Ne,¹⁹F)¹¹⁷In one-proton transfer reactions at 15 AMeV incident energy.

The MAGNEX magnetic spectrometer is nowadays used in the experimental measurements of rare quasi-elastic reactions between heavy ions at intermediate energy within the NUMEN project. The small cross sections involved in such processes under the large yields due to competitive reaction channels have motivated an accurate control of the background sources. In such view, the not ideal particle identification could introduce spurious contributions which have been identified and evaluated in the present analysis.