Determination of the link between heavy ion charge exchange reactions and single and double beta decay matrix elements

We performed theoretical studies on Heavy ion charge exchange reactions, at low energies, focusing on the interplay between nuclear structure and reaction dynamics. Such studies allow also to enlight the existence of a relation between Heavy ion double charge exchange (HIDCE) cross section at forward scattering angles and double beta ($\beta\beta$) decay nuclear matrix element (NME) of the target or projectile nucleus considered. HIDCE reactions can be described as a sequence of two single charge changing processes, which can be correlated or not, thus mimicking $0\nu\beta\beta$ and $2\nu\beta\beta$ decays, respectively. The dominance of the former mechanism would allow to gain information on $0\nu\beta\beta$ NME, thus in turn allowing to determine neutrino Majorana mass with a significant accuracy, if such weak decay were observed.