Multiple diffraction theory, optical potentials, and an alternative approach to high-energy scattering by nuclei

Abstract

Aformally exact perturbation expansion of the high-energy scattering amplitude by nuclei is developed, in which the leading term is given by the Glauber's multiple diffraction amplitude. The leading correction terms are examined in detail, which deal with the two approximations involved in the Glauber amplitude; (a) the linearization of the Green's function and (b) the fixed-scatterer assumption. Thus, the diffraction amplitude can be systematically improved rather simply so long as the scattering angle is not too large. It is stressed that, when the target profile function is replaced by the individual mucleon profiles, the correction to the linearization approximation is automatically included to all orders in the Glauber amplitude, insofar as the nonoverlapping interactions are concerned. The contents of the Glauber wave function are then analyzed to show explicitly that, within the approximations (a) and (b), the major part of the inelastic channel information, and thus of the optical potential, is already included in the theory. By comparing the diffraction theory with the optical potential approach, which is based on the multiple scattering theory and the conversion of the optical potential to a set of coupled equations, we exhibit a close connection between the two seemingly diverging approaches. As a result of this analysis, we derive a modified theory of high-evergy scattering by nuclei, in which the elastic component is to be treated exactly without the linearization while the inelastic component is taken directly from the diffraction theory.