Transfer reactions between odd-odd and even-even nuclei by using IBFFM

Abstract: Spectroscopic Amplitudes (SA) in the Interacting Boson Fermion Fermion Model (IBFFM) are necessary for the computation of $0\nu\beta\beta$ decays but also for cross sections of heavy-ion reactions, in particular, Double Charge Exchange reactions for the NUMEN collaboration, if one does not want to use the closure limit. We present for the first time: i) the formalism and operators to compute in a general case the spectroscopic amplitudes in the scheme IBFFM from an even-even to odd-odd nuclei, in a way suited to be used in reaction code, i.e., extracting the contribution of each orbital; 2) the odd-odd nuclei as described by the old IBFFM are obtained for the first time with the new implementation of Machine Learning (ML) techniques for fitting the parameters, getting a more realistic description. The one body transition densities for $^{116}$Cd $\rightarrow$ $^{116}$In and $^{116}$In $\rightarrow$ $^{116}$Sn are part of the experimental program of the NUMEN experiment, which aims to find constraints on Neutrinoless double beta decay matrix elements.