A joint analysis of the elastic-scattering angular distributions and fusion cross sections together with the S factor for the O16+O16 system near and below the Coulomb barrier is reported. To describe these observables within the framework of the optical model, a comparative study of microscopic $\alpha${}-$\alpha${} double-folding clusters and phenomenological shallow potentials with surface-transparent imaginary parts is performed. Although the phenomenological Woods-Saxon type of shallow real potentials is unable to provide a consistent explanation of these data, the $\alpha${}-$\alpha${} double-folding cluster potential obtained by considering the $\alpha${}-cluster structure of O16 provides a considerable improvement. The $\alpha${}-$\alpha${} double-folding cluster potential also reproduces the normalized resonant energy states of S32 for the N=24 cluster band.

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.

The goal of NUMEN project is to access experimentally driven information on Nuclear Matrix Elements (NME) involved in the neutrinoless double beta decay (0νββ) by accurate measurements of the cross sections of heavy-ion induced double charge-exchange reactions. In particular, the (¹⁸O,¹⁸Ne) and (²⁰Ne,²⁰O) reactions are adopted as tools for β⁺β⁺and β⁻β⁻decays, respectively. The experiments are performed at INFN–Laboratory Nazionali del Sud (LNS) in Catania using the Superconducting Cyclotron to accelerate the beams and the MAGNEX magnetic spectrometer to detect the reaction products. The measured cross sections are very low, limiting the present exploration to few selected isotopes of interest in the context of typically low-yield experimental runs. In order to make feasible a systematic study of all the candidate nuclei, a major upgrade of the LNS facility is foreseen to increase the experimental yield by more than two orders of magnitude. To this purpose, frontier technologies are being developed for both the accelerator and the detection systems. An update description of the NUMEN project is presented here, focusing on recent achievements from the R&D activity.