The nuclear matrix elements of 0νββ decay and the NUMEN project at INFN-LNS

An innovative technique to access the nuclear matrix elements entering the expression of the life time of the double beta decay by relevant cross sections measurements of double charge exchange reactions is proposed. The basic point is the coincidence of the initial and final state wave-functions in the two classes of processes and the similarity of the transition operators, which in both cases present a superposition of Fermi, Gamow-Teller and rank-two tensor components with a relevant implicit momentum transfer. A key aspect of the project is the use of the MAGNEX large acceptance magnetic spectrometer, for the detection of the ejectiles, and of the LNS K800 Superconducting Cyclotron (CS), for the acceleration of the required high resolution and low emittance heavy-ion beams. The upgrades of both MAGNEX and CS are necessary to reach the optimal experimental conditions