Compound Nuclear Theory and the Optical Model

A formalism is developed to relate the total cross section for low-energy nucleon-nucleus scattering to the cross section due to a potential well. By introducing the intermediate model of Lane, Thomas and Wigner for the compound nucleus states, a simple relation between these two cross sections is obtained. The method of extracting a potential well to replace the hard sphere scattering and the scattering from `far distant' levels is given and then extended to find the well which describes the average total cross section.