Critical Stability in Nuclei ? An Old Problem Revisited

Abstract

In this paper we will focus on the nucleon-nucleon interaction in relative S-states. The 1S0 interaction is known to be close to that for critical two-body binding. We will discuss two approaches to the NN interaction, which are equivalent on-shell but not off-shell. There is a well-defined transformation between these approaches [1]. One (my preferred approach) is to minimize the tensor forces far off-shell, which leads to more rapid convergence, but at the price of significant non-locality. This approach is used in a model of relativistic tensor quenching of OPEP [2]. With non-local NN interactions it is possible to fit not only NN observables, but also the NNN ground-state energies [3]. The other approach is to maximize the role of the π and keep the interaction as local as possible [4]. This approach is also internally consistent, but requires additional NNN interactions to fit nuclear data. Also, we discuss briefly a so-called low momentum interaction [5, 6], which fits S-wave phase shifts quite well. This interaction is strongly non-local, and it can be approximated by a schematic separable interaction. Finally, we mention the Nambu–Jona-Lasinio model [7] and a good approximation, the Hulthen potential, which provides some insight into the near critical two-body binding.