Coupling schemes and effective interactions in the nuclear shell model

A simple form of effective nuclear interaction, which has many of the features of the interaction derived from nucleon-nucleon scattering experiments, is considered. This model force operates only in l=0 states of relative motion of two nucleons. The consequences of such an s state interaction model (SIM) are explored, and it is shown that important coupling schemes (such as a pairing scheme and the Elliott scheme) follow as special versions of this model. The role of the repulsive core in nuclear forces and its relationship to the Elliott scheme are demonstrated. Two-nucleon and four-nucleon spectra in the 0d1s shell are calculated with such forces and the results are compared with observed level schemes of O18, F18, O20 and Ne20. The fairly good agreement with the observed levels provides some indication of the nature of the effective interaction operative in the 0d1s shell