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Multi-channel experimental and theoretical constraints for the $^{116}$Cd($^{20}$Ne,$^{20}$F)$^{116}$In charge exchange reaction at 306 MeV

Charge exchange (CE) reactions offer a major opportunity to excite nuclear isovector modes, providing clues about the nuclear interaction in the medium. Moreover, double charge exchange (DCE) reactions are proving to be a tempting tool to access nuclear transition matrix elements (NME) related to double beta-decay processes. Through a multi-channel experimental analysis and a consistent theoretical approach of the $^{116}$Cd($^{20}$Ne,$^{20}$F)$^{116}$In single charge exchange (SCE) reaction at 306 MeV, we aim at disentangling from the experimental cross section the contribution of the competing mechanisms, associated with second or higher order sequential transfer and inelastic processes. We measured excitation energy spectra and absolute cross sections for elastic + inelastic, one-proton transfer and SCE channels, using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. For the first two channels, we also extracted the experimental cross section angular distributions. The experimental data are compared with theoretical predictions obtained by performing two-step distorted wave Born approximation and coupled reaction channel calculations. We employ spectroscopic amplitudes for single-particle transitions derived within a large-scale shell model approach and different optical potentials for modeling the initial and the final state interactions. The present study significantly mitigates the possible model dependence existing in the description of these complex reaction mechanisms, thanks to the reproduction of several channels at once. In particular, our work demonstrates that the two-step transfer mechanisms produce a non negligible contribution to the total cross section of the $^{116}$Cd($^{20}$Ne,$^{20}$F)$^{116}$In reaction channel, although a relevant fraction is still missing, being ascribable to the direct SCE mechanism, which is not addressed here.