Regge Description of Optical-Model Scattering

The analytic continuation of the $S$ matrix into the complex angular momentum plane is performed exactly for the Woods-Saxon-type optical potentials, describing the elastic scattering of spinless but charged particles. The properties of this $S$ matrix, such as the nature of the pole trajectories and the behavior of the background integral, are investigated for several specific cases. Based on these exact calculations, the validity of various approximations made in the Regge theory is assessed. It is found that approximations which retain only the pole terms are generally poor, being quite sensitive to the number and the positions of the poles and converging very slowly with an increasing number of poles. On the other hand, models using a simple analytic background term, in addition to one pole term, are found to reproduce the exact Regge amplitude quite accurately under favorable conditions. Suggestions are made for the possibility of extending this idea into a background-plus-several-pole model, when the background-one-pole model fails.