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.

Background: An accurate description of the initial and final state interactions in the ${}^{18}\mathrm{O}+{}^{76}\mathrm{Se}$ collision is demanded by the NUMEN project. The study of single and double charge exchange nuclear reactions is the main purpose for NUMEN, since these can be used as tools to provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-$\beta$ decay. To date, the details of the optical potentials and nuclear response to isospin operators for many of the projectile-target systems proposed for the NUMEN double charge exchange studies are poorly known. The ${}^{18}\mathrm{O}+{}^{76}\mathrm{Se}$ case, here under study, is particularly relevant due to its connection with the ${}^{76}\mathrm{Ge}$ neutrinoless double-$\beta$ decay.

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.

Background: Single-charge-exchange reactions are appropriate tools to study the nuclear response to one-particle/one-hole isospin probes, gaining additional interest from the connection to beta decay. This analogy has been recently extended to second order, connecting double-charge-exchange reactions and double beta decays. Nowadays, the availability of powerful experimental setups and advanced nuclear theories and models allows one to access precious information on key nuclear structure aspects embedded in the widely sought neutrinoless double beta decay.

The present article reports new data on the ${}^{48}\mathrm{Ti}({}^{18}\mathrm{O},{}^{17}\mathrm{O}){}^{49}\mathrm{Ti}$ reaction at 275 MeV incident energy as part of the systematic research pursued within the NUMEN (NUclear Matrix Elements for Neutrinoless double $\beta$ decay) project. Supplementary measurements of the same reaction on ${}^{16}\mathrm{O}$ and ${}^{27}\mathrm{Al}$ targets were also performed in order to estimate the background arising from the use of a composite target (${\mathrm{TiO}}_2+{}^{27}\mathrm{Al}$). These data were analyzed under the same theoretical framework as those obtained with the titanium target in order to reinforce the conclusions of our analysis. Differential cross-section angular distribution measurements for the ${}^{17}\mathrm{O}^{8+}$ ejectiles were performed in a wide angular range by using the MAGNEX large acceptance magnetic spectrometer. The experimental results were analyzed within the distorted-wave and coupled-channels Born approximation frameworks. The optical potentials at the entrance and exit channels were calculated in a double folding approach adopting the São Paulo potential, and the spectroscopic amplitudes for the projectile and target overlaps were obtained from large-scale shell model calculations. The differential cross sections are well described by the theoretical calculations, where a weak coupling to collective excitations of projectile and target is inferred. The sensitivity of transfer cross sections on different model spaces adopted in nuclear structure calculations is also discussed.