Relationship Between the Optical Model and the Resonance Theory

Abstract

The relationship between cross sections and the strength function is discussed. The usually used simple linear relation is shown to be an approximation to the more general theory of Wigner and Eisenbud. With this theory, a consistent and simple behavior of the strength function with respect to the energy and the atomic weight can be obtained. The problems of the proper choice of the boundary condition and the matching radius for the diffuse well are discussed. A quantitative estimate of the effect of the nonlinear terms in a typical nucleus ${\mathrm{Nb}}^{93}$ is presented.