The Inelastic Scattering of Nucleons by the Surface Interaction

The effect of the surface interaction, based on A. Bohr's collective model, on the inelastic scattering of nucleons by a nucleus at medium energy is discussed. The wave function is expressed as a sum of amplitudes, which correspond to various states of target nucleus and incident nucleon. From the Schrodinger equation one can derive a set of coupled equations for the amplitudes, which correspond to a state of the surface excitation while the effect of the other amplitudes is replaced by distorting potentials. The interaction between the states considered explicitly is assumed as the surface interaction proposed by A. Bohr, and taken to have a δ-function type radial dependence. The coupled equations are solved without further approximation. The distorting potential is chosen so as to give the right result for the elastic scattering in the presence of the surface interaction. If that interaction is strong enough, the distorting potential differs considerably from the usual optical potential, which would give a good result for the elastic scattering in the absence of surface interaction. The theory is applied to proton scattering by 24Mg at 10 MeV, and the result shows that the strong angular dependence of the inelastic scattering is due to the surface interaction while the main contribution comes from the compound nucleus.