Two body perturbing resonances in a three body system: origin of σ-meson in n-n interaction

There are many missing links in the nuclear structure many body problems, such as the treatment of the repulsive core part of the N-N interaction, inclusion of non-perturbative effects in the many body solution, proper inclusion of tensor interaction, in the field theoretic formulation the necessity yet still unobserved σ-meson and many other such problems. One of the most intriguing problems is to explain the elusiveness of the σ-meson, supposed to be a two-pion resonance which has not been seen in the π - π scattering experiments. The σ-meson is a requirement even for the explanation of the N-N scattering data. It is usually argued that it may be too broad a resonance or that it may be manifestation of an approximation to the dominant contribution in the two pion exchanges. If its mass together with the coupling constants for all the other mesons are fitted to the experimental N-N scattering data then they can be reproduced well in the OBEP potential