The FDS (Fermion Dynamical Symmetry) Model, Nuclear Shell Model and Collective Nuclear Structure Physics*

Abstract

We often hear nowadays that the “fundamental theory of strong interaction physics is QCD”. All the models and theories in that field are motivated by it. Nevertheless, due to the enormous complexities of QCD, one still awaits its precise usage in practical calculations. In nuclear structure physics, there is a parallel dilemma. The fundamental theory of nuclear structure is the shell model. Let me be precise about this. By the term shell model, I mean the diagonalization of a nuclear hamiltonian with certain residual “effective” Interactions in a truncated many body basis which Is constructed from the spherical single particle orbits truncated within, say, one major physical shell. This is nuclear structure physics’ utopia. Unfortunately, while the shell model has proven to be extremely useful for studying properties of nuclei near closed shells, its general practice for systems with large number of valence nucleons has been the major challenge in the nuclear structure physics arena for the last thirty years. In order to use the shell model to study such systems where very “rich physics” presides, further drastic truncation of the space is a must. Therefore, how to further truncate the fermion space is perhaps the central question. In this talk, I hope to convince you that, through twists and turns, the idea of dynamical symmetry has played a pivotal role in this entire effort and that we may now have a glimpse as to how this further truncation of the shell model space can be achieved. We may be at the verge of entering a new stage of nuclear structure physics where one is able to reconcile on the one hand the collective nuclear structure physics with, on the other the spherical shell model.