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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

We report on first-principles band-structure calculations of the semiconducting CuAlO2 delafossite compound in the pure form and also with Cd impurity occupying either a Cu or Al position. The computational tool was a full-potential linear augmented plane-wave method, with the generalized gradient approximation accounting for the exchange and correlation effects. The changes caused by the presence of Cd are studied by the analysis of the electronic structure and the electric field gradient (EFG) in both Cd-doped and pure CuAlO2 systems. Good agreement between the calculated and measured EFGs at Cd substituting for Cu or Al atoms in CuAlO2 indicates that the calculations were able to correctly describe the ground state of the system containing the impurity. It is shown that a specific hybridization scheme, involving Cu (and Cd) s and dz2 orbitals and neighbouring O pz orbitals, takes place at the Cu sites in CuAlO2 as proposed earlier. The results of the calculations indicate that the Cd-doped system changes its electrical properties when Cd replaces Cu atoms (producing an n-type semiconductor), but not when it substitutes for Al atoms.