Off-Shell Behavior of the Nucleon-Nucleon Interaction

Abstract

The nuclear force is conventionally treated in a nonrelativistic framework and represented by a potential model. The potential may be deduced from theory, or be a phenomenological fit to certain nuclear data. In practice, any realistic potential that fits the two-body data well contains some measure of phenomenology. That the resulting model is far from unique is all too obvious from the literature [see, for example, the review by Moravcsik (Mor 72)]. It became evident at an early stage, chiefly through a study of nuclear matter, that these different potential models can predict quite different results in many-body calculations. Even if the fits to data on the two-body problem—so-called on-energy-shell data—were identical, different models can still disagree when compared in many-body calculations. This is because in a many-body situation, although energy and momentum must be conserved overall, they need not be conserved in every two-body interaction. Thus one requires the off-energy-shell matrix elements. This realization has prompted a great body of work aimed at understanding the degree of off-energy-shell liberty in the NN force and its importance for various nuclear many-body problems. This chapter is a review and consolidation of this work. We believe that it is opportune to review this work now, while the existing literature, though voluminous, is still manageable. Many facets of the problem are understood, and we have reached a stage where extensions of the nonrelativistic potential model are required.