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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.

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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.

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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.