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A Statistical Description of Nuclear Reaction Models for Medical Radionuclides: the Paradigmatic Case of $^{47}$Sc Production with Thick Vanadium Targets

We have introduced a tool to describe in a simple and efficient way the outcomes of known nuclear reaction codes. It differs from the customary use where typically a specific single model is selected and the remaining disregarded. The use of simple statistical procedures allows to introduce a more general theoretical evaluation with quantitative uncertainty, constructed on the variability of the built-in theoretical models. We apply the technique to study the production of $^{47}$Sc (a radio-nuclide with potential theranostic applications in nuclear medicine) with a proton beam impinging on a thick natural Vanadium target. We find an energy range with significant production of $^{47}$Sc, and a minimum co-production of $^{46}$Sc, the radioactive contaminant that has to be avoided as much as possible because of its much longer half life than $^{47}$Sc (83.79 d vs 3.3492 d).