The Semi-Classical Model for the Nuclear Reaction at Intermediate Energies

Abstract

A formalism is presented for the distorted wave approximation for the inelastic scattering of nucleons by nuclei at intermediate energies which lead to the continuous excited states of the residual nucleus. On the a sumption of semi- classical approximation for the disto ted waves of the incoming and outgoing particles, the Tho sFermi model for the nucleus, and the short range of the interaction, the cross section is obtained in a closed form as the sum of local collisions at all the points within the nucleus, wbich are given by the two nucleon cross sections averaged over the momentum distribution of the targer nucleons multiplied by the penetrating and the escaping probability of the incident and the emitted particle, respectively. The localization of the collision is due to the average procedure over the final states of the nucleus. The semiclassical method of approximation for the distorted wave in the complex distorting potential is successfully performed by generalizing the geometrical optics'' approximation for a real distorting potential. The resulting expression permits a very simple, intuitive interpretation. Discussions on the validity of the approximations used in the derivation are given. (auth)