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

We discuss modeling of nuclear structure beyond the 2-body interaction paradigm. Our first example is related to the need of three nucleon contact interaction terms suggested by chiral perturbation theory. The relationship of the two low-energy effective coupling parameters for the relevant three nucleon contact 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 parameter region has been illustrated using the binding energy of $^4$He. Further justification of A-body interaction terms is outlined based on the Okubo-Lee-Suzuki effective interaction method used in solving the nuclear many-body problem within a finite model space. The third example we use is an exactly solvable A-body extended paring interaction applied to heavy nuclei with a long isotopic chains, in particular using $^{132}$Sn and $^{208}$Pb as closed core system illustrates a remarkable relationship between the extended pairing strength $G(A)$ and the size of the valence space $\dim(A)$ for the members 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 better understanding of the three-nucleon (NNN), four-nucleon (NNNN), and A-body interactions in nuclei either derived from ChPT or from a phenomenological considerations.