Theory of High-Energy Diffraction Scattering. II

Abstract

In this paper we extend the treatment in Paper I of this series by studying high-energy scattering processes from the viewpoint of the projectile system, i.e., the system in which the incident particle is at rest. In particular, we give two equivalent sets of rules for obtaining the high-energy scattering amplitudes from this standpoint, one for the momentum space and the other for the position space. It is found that both sets of rules give directly the exact expression of the impact factor, and no more approximations need to be made even for the numerators of the integrals involved. We conclude that the impact factor is best studied in the projectile system, while the potential is most conveniently taken care of in the laboratory system, and that they can be separately treated. In the case of high-energy collision of two particles, each impact factor is best studied in its own projectile system. These two sets of rules are shown to be equivalent to those in the laboratory system. In the Appendix we also study high-energy scattering processes in the position space from the viewpoint of the laboratory system, and explicit rules are given.