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We discuss modeling of nuclear structure beyond the 2-body interactionparadigm. Our first example is related to the need of three nucleon contactinteraction terms suggested by chiral perturbation theory. The relationship ofthe two low-energy effective coupling parameters for the relevant three nucleoncontact interaction terms $c_D$ and $c_E$ that reproduce the binding energy of$^3$H and $^3$He has been emphasized and the physically relevant parameterregion has been illustrated using the binding energy of $^4$He. Furtherjustification of A-body interaction terms is outlined based on theOkubo-Lee-Suzuki effective interaction method used in solving the nuclearmany-body problem within a finite model space. The third example we use is anexactly solvable A-body extended pairing interaction applied to heavy nucleiwith a long isotopic chains, in particular using $^{132}$Sn and $^{208}$Pb asclosed core system illustrates a remarkable relationship between the extendedpairing strength $G(A)$ and the size of the valence space $\dim(A)$ for themembers of these two isotope chain: $G(A)=\alpha\dim(A)^{-\beta}$ with$\alpha=259.436$ for Sn and $\alpha=366.77$ for Pb while the parameter $\beta$is practically 1. These three cases present evidence for the need of betterunderstanding of the three-nucleon (NNN), four-nucleon (NNNN), and A-bodyinteractions in nuclei either derived from ChPT or from a phenomenologicalconsiderations.

Beyond the 2-Body Interaction Paradigm: The Case for Extended A-Body Pairing Interaction in Nuclei