Background: In our recent work [M. J. Ermamatov et al., Phys. Rev. C 94, 024610 (2016)], the two-neutron transfer induced by the $({}^{18}\mathrm{O},{}^{16}\mathrm{O})$ reaction was studied for ${}^{16}\mathrm{O}$ nucleus. Theoretical analysis of the low-lying states of ${}^{18}\mathrm{O}$ indicates that the transfer to the ground state proceeds predominantly through simultaneous transfer of the two-neutron system.

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 ${}^{10}\mathrm{B}+{}^{120}\mathrm{Sn}$ reaction has been investigated at $E_{\mathrm{Lab}}=37.5$ MeV. The cross sections for different channels, such as the elastic scattering, the excitation of the $2^{+}$ and $3^{-}{}^{120}\mathrm{Sn}$ states, the excitation of the $1^{+}$ state of ${}^{10}\mathrm{B}$, and the $1n$ pick-up transfer, have been measured. One-step distorted-wave Born approximation and coupled-reaction-channels calculations have been performed in the context of the double-folding São Paulo potential. The effect of coupling the inelastic and transfer states on the angular distributions is discussed in the paper. In general, the theoretical calculations within the coupled-reaction-channels formalism yield a satisfactory agreement with the corresponding experimental angular distributions.

Experimental angular distributions for the ${}^7\mathrm{Li}+{}^{120}\mathrm{Sn}$ elastic and inelastic (projectile and target excitations) scattering, and for the neutron stripping reaction, have been obtained at $E_{\mathrm{LAB}}=20$, 22, 24, and 26 MeV, covering an energy range around the Coulomb barrier $(V_B^{\left(\mathrm{LAB}\right)}\approx 21.4$ MeV). Coupled channel and coupled reaction channel calculations were performed and both describe satisfactorily the experimental data sets. The ${\frac{1}{2}}^{-}$ state ${}^7\mathrm{Li}$ inelastic excitation (using a rotational model), as well as the projectile coupling to the continuum $(\alpha$ plus a tritium particle) play a fundamental role on the proper description of elastic, inelastic, and transfer channels. Couplings to the one-neutron stripping channel do not significantly affect the theoretical elastic scattering angular distributions. The spectroscopic amplitudes of the transfer channel were obtained through a shell model calculation. The theoretical angular distributions for the one-neutron stripping reaction agreed with the experimental data.