NUCLEAR-REACTION THEORY OF RESONANCES AND SURFACE-WAVES

The theory of resonances, regarded as singularities in the complex angular-momentum plane, is here reconsidered taking into account the role played by the so-called <<echoes>> of resonances. In this way we may describe sequences of resonances and echoes. As a typical example we consider the rotational band produced by the He-4-He-4 elastic scattering. In this theory the poles of the S-function describe families of resonances and are related to the symmetries underlying the dynamics. In order to exhibit this connection we approach the many-body problem by the use of the <<grand-angular-momentum tensor>>. We show, in detail, how various rotational bands emerge in three-body problem. The extension of the analysis to many-body problem is outlined. Furthermore by the use of collective coordinates we briefly illustrate how rotational excitations can be described as hydrodynamical vortices, obtaining a model which fits the complex angular-momentum picture of resonances. At higher energies the resonances smear out towards diffractive effects like the surface waves; this process is described by the motion of poles in the complex angular-momentum plane. Using the ray-tracing method, in the spirit of Keller geometrical diffraction theory, a detailed analysis of surface waves, and of the related phenomena like caustics and rainbows, is developed.