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Via the construction of a functor from $\mathsf{C}_{u}(H)$ to an auxiliarycategory we associate, with any triplet $(G,F,\rho)$, two naturaltransformations, $\mathfrak{m}_{\star}$ morphism of$\mathsf{Fct}(\mathsf{C}_{u}(H)^{op},\mathsf{Fct}(H,\mathsf{set}))$ and$\mathfrak{v}_{\natural}$ morphism of$\mathsf{Fct}(\mathsf{C}_{u}^{0}(H)^{op},\mathsf{Fct}(H,\mathsf{set}))$. $G$and $F$ are locally compact groups, $\rho:F\to Aut(G)$ is a continuousmorphism, $H$ is the external topological semidirect product of $G$ and $F$relative to $\rho$, $\mathsf{C}_{u}^{0}(H)$ is a subcategory of$\mathsf{C}_{u}(H)$ a subcategory of the category of $C^{\ast}-$dynamicalsystems with symmetry group $H$ and equivariant morphisms. For $\mathfrak{A}$in $\mathsf{C}_{u}^{0}(H)$ to assemble $\mathfrak{m}_{\star}^{\mathfrak{A}}$ weexploit the Connes characters generated by JLO cocycles $\Phi$ on theunitization of certain $C^{\ast}-$crossed products relative to $\mathfrak{A}$,while to construct $\mathfrak{v}_{\natural}^{\mathfrak{A}}$ we exert the statesof the $C^{\ast}-$algebra underlying $\mathfrak{A}$ associated in a convenientmanner with the $0-$dimensional components of the $\Phi$'s. Being$\mathsf{C}_{u}(H)$ the category of fissioning systems, we use$\mathfrak{m}_{\star}^{\mathfrak{A}}$ and$\mathfrak{v}_{\natural}^{\mathfrak{A}}$ to define the nucleon phases and thefragment states resulting next the fission processes of the fissioning system$\mathfrak{A}$ occur. We apply the naturality of $\mathfrak{m}_{\star}$ and$\mathfrak{v}_{\natural}$ to establish the universality of the global nucleonmasses and the global Terrell law, stated as invariance of the light and heavynucleon core masses and invariance of the prompt-neutron yield undercontrovariant action of $\mathsf{C}_{u}^{0}(H)$ and under action of $H$ overthe field of fission processes.

Natural transformations associated with a locally compact group and universality of the global Terrell law