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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

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 *

Abstract:In this paper, we present the status of the line for laser-driven light ions acceleration (L3IA) currently under implementation at the Intense Laser Irradiation Laboratory (ILIL), and we provide an overview of the pilot experimental activity on laser-driven ion acceleration carried out in support of the design of the line. A description of the main components is given, including the laser, the beam transport line, the interaction chamber, and the diagnostics. A review of the main results obtained so far during the pilot experimental activity is also reported, including details of the laser-plasma interaction and ion beam characterization. A brief description of the preliminary results of a dedicated numerical modeling is also provided.