Elastic scattering is in some sense the most fundamental type of reaction, but it is also the most difficult to understand theoretically. There is a huge amount of spin-dependent data at low to medium energies, but little understanding of the mechanisms at work. In several instances, however, spin-dependent data have played a crucial rôle in nailing the coffin of a current theoretical picture. Somehow, simple-minded ideas, which succeed in explaining gross features of cross-sections, angular distributions etc., run aground when faced with the more probing questions involved in spin-dependent reactions. Because of the lack of clear-cut theoretical ideas and because of the difficulty of the experiments there has generally been a lack of experimental effort in this field since the mid-1980s, but this situation is about to change with the commissioning of the RHIC collider at Brookhaven. There, besides a major programme of heavy-ion physics, it will be possible to study pp collisions, with both beams polarized and up to an energy of 250 GeV per beam. Consequently we shall concentrate in this chapter on nucleon–nucleon scattering.

Broadly speaking there are two kinematic regions of interest, small to medium values of momentum transfer and large momentum transfer. The first is, strictly speaking, in the domain of non-perturbative QCD, so there are no precise theoretical predictions, though there are very interesting suggestive hints. In the second region perturbative QCD ought to be applicable and, indeed, very powerful theoretical results have been derived.