Momentum space folding model for heavy ion scattering (I). General formalism and real potential

Abstract

A model is developed in which the complex optical potential for heavy ion scattering can be expressed as a folding integral over reaction matrix elements for bound nucleons in momentum space. For the nuclei the Thomas-Fermi model is employed in the local density approximation. A heuristic prescription is given so that the Pauli principle is fulfilled in the overlap region. With the help of the optical theorem, it is shown that the imaginary potential depends essentially on the density distributions of the fragments and the total cross sections for the scattering of bound nucleons. For the real part of the potential the nucleon-nucleon interaction is treated in the Scott-Moszkowski separation method. The excitation functions for 16O-16O and 12C-12C scattering are calculated. Finally both the radial shapes and the energy dependence of the optical potential are discussed.