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 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 270 MeV, give encouraging indication on the capability of the proposed technique to access relevant quantitative information.The two major aspects 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 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.3

The 10 B + 120 Sn reaction has been investigated at E Lab = 37.5 MeV. The cross sections for different channels, such as the elastic scattering, the excitation of the 2 + and 3 − 120 Sn states, the excitation of the 1 + state of 10 B, and the 1n pick-up transfer, have been measured. One-step distorted-wave Born approximation and coupled-reactionchannels 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.

We present new experimental angular distributions for the elastic scattering of 6 Li + 120 Sn at three bombarding energies. We include these data in a wide systematic involving the elastic scattering of 4,6 He, 7 Li, 9 Be, 10 B and 16,18 O projectiles on the same target at energies around the respective Coulomb barriers. Considering this data set, we report on optical model analyses based on the double-folding São Paulo Potential. Within this approach, we study the sensitivity of the data fit to different models for the nuclear matter densities and to variations in the optical potential strengths.

Background: In our recent work [M. J. Ermamatov et al., Phys. Rev. C 94, 024610 (2016)], the two-neutron transfer induced by the ( 18 O, 16 O) reaction was studied for 16 O nucleus. Theoretical analysis of the low-lying states of 18 O indicates that the transfer to the ground state proceeds predominantly through simultaneous transfer of the two-neutron system. Purpose: In this work, we extend our previous theoretical analysis towards high-lying states of the 18 O nucleus. In order to achieve a comprehensive picture, we revisit the experimental data for the 16 O(t,p) 18 O reaction at 15 MeV bombarding energy. We also include new experimental cross sections for the high-lying states of the 18 O residual nucleus, populated in the 16 O( 18 O, 16 O) 18 O reaction at 84 MeV. Method:The same spectroscopic parameters of the target nucleus were used as input in the coupled channel calculations for the transfer induced by triton and 18 O projectiles. Simultaneous two-neutron transfer is calculated within the coupled reaction channel approach, using the extreme cluster and independent coordinate models. The sequential process is calculated within the distorted-wave Born approximation. Results: Theoretical calculations reproduce the 16 O(t,p) 18 O data well, leading to natural parity states in the 18 O nucleus without the need of adjustable parameters. The same methods are applied to the 16 O( 18 O, 16 O) 18 O data and a good agreement is observed. Conclusions: Detailed analyses show the importance of a simultaneous mechanism for the two-neutron transfer reactions. In transferring two neutrons, the pairing correlation plays an important role.

Experimental angular distributions for the 7 Li + 120 Sn elastic and inelastic (projectile and target excitations) scattering, and for the neutron stripping reaction, have been obtained at E LAB = 20, 22, 24, and 26 MeV, covering an energy range around the Coulomb barrier (V (LAB) B ≈ 21.4 MeV). Coupled channel and coupled reaction channel calculations were performed and both describe satisfactorily the experimental data sets. The 1 2 − state 7 Li inelastic excitation (using a rotational model), as well as the projectile coupling to the continuum (α 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.

Background: Heavy-ion induced two-nucleon transfer reactions are powerful tools to reveal peculiar aspects of the atomic nucleus, such as pairing correlations, single-particle and collective degrees of freedom, and more. Also, these processes are in competition with the direct meson exchange in the double charge exchange reactions, which have recently attracted great interest due to their possible connection to neutrinoless double-β decay. In this framework, the exploration of two-nucleon transfer reactions in the 20 Ne + 116 Cd collision at energies above the Coulomb barrier is particularly relevant since the 116 Cd nucleus is a candidate for the double-β decay.Purpose: We want to analyze selected transitions to low-lying 0 + and 2 + states of the residual nuclei in the 116 Cd( 20 Ne, 22 Ne) 114 Cd two-neutron pickup and 116 Cd( 20 Ne, 18 O) 118 Sn two-proton stripping reactions at 306 MeV incident energy and determine the role of the couplings with inelastic transitions. Methods: We measured the excitation energy spectra and absolute cross sections for the two reactions using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. We performed direct coupled reaction channels and sequential distorted wave Born approximation calculations using the double folding São Paulo potential to model the initial and final state interactions. The spectroscopic amplitudes for two-and singleparticle transitions were derived by different nuclear structure approaches: microscopic large-scale shell model, interacting boson model-2 and quasiparticle random phase approximation. Results:The calculations are able to reproduce the experimental cross sections for both two-neutron and twoproton transfer reactions. The role of couplings with the inelastic channels are found to be important in the two-proton transfer case. A competition between the direct and the sequential process is found in the reaction *

Elastic scattering measurements were performed for the 7 Li +p system in inverse kinematics at energies of 16, 25, 35, and 38.1 MeV and for the 7 Li +d system at 38.1 MeV. The heavy ejectiles were detected by the large acceptance MAGNEX spectrometer at the Laboratori Nazionali del Sud in Catania, Italy. The results are analyzed using the Jeukenne-Lejeune-Mahaux and continuum discretized coupled channel frameworks. In the latter case the cluster structure of 7 Li proves to be critical for the theoretical interpretation of the experimental results.