Calculations of Cohen＇s nuclear Fukui function and softness are presented for a sample set of diatomic molecules. The obtained results were interpreted using Berlin＇s theorem of binding and antibinding molecular regions. Moreover, new relations among the nuclear reactivity descriptors were derived within the four ensembles of density functional theory; a definition was provided for the nuclear hardness kernel, in accordance with Cohen＇s nuclear softness kernel. It turned out that local hardness can be connected with this nuclear hardness kernel, strengthening the idea that local hardness should be considered as a nuclear reactivity index, whereas local softness is an electronic reactivity index.