Problems in many-body effective interaction theory for nuclei and how they differ from those for atoms

The many-body perturbation theory for open-shell systems is briefly discussed, particularly with regard to the derivation of the diagrammatic expansion for the effective interaction. We then compare the application of this theory to atoms and to nuclei and observe that calculations are more difficult for nuclei. Most of the problems in the nuclear calculations arise from the complicated nature of the nucleon-nucleon (or strong) interaction. In particular the diagrammatic expansion for the nuclear effective interaction tends to diverge due to highly collective nuclear states which lie low in energy, because of the nature and strength of the nucleon-nucleon interaction. Other methods for calculating the effective interaction besides perturbation theory are also discussed. At the present time the exp (S) or coupled-cluster method appears to be the best and the most accurate method for computing nuclear spectra.