Effects of quantum diffraction in statistical theories of heavy ion reactions. Pt. 1

We describe effects of quantum diffraction in a statistical theory of heavy ion reactions on the basis of semi-classical approximations and subsequent averaging over ensembles of microscopic final channels. Two types of quantum phenomena are accounted for: the interferences close to a rainbow angle, and the diffraction produced by a rapid onset of absorption into fusion channels for small impact parameters. The quantal corrections are expressed by functionals of an average deflection function which can be calculated from the knowledge of a macroscopic classical distribution function. No assumptions concerning the nature of this coarse distribution are made except for the fact that it must be classical as far as the relative motion of the nuclei is concerned. (orig.)