Zero-Energy Scattering of Neutrons by Optical Models

Abstract

If the imaginary part of the complex square-well potential is adjusted to produce the correct-sized giant resonances in the total cross sections of light nuclei, it is found to be too large to do the same for heavy nuclei and too small throughout most of the range of mass numbers to produce a suitable zero-energy strength function. Damping of giant resonances from optical potentials can generally be correlated with that of a zero-energy scattering amplitude, and the square well defects mentioned can all be studied with analytic simplicity at zero energy. When total cross-section data matching is performed for a square-well or a diffuseedged potential, the imaginary part will be much less dependent on mass number if it is concentrated into a surface layer. However, once the parameters of any reasonable spherically symmetric potential have been determined from matching total cross sections, a general relationship prohibits complete experimental agreement with the zero energy strength function. For certain potentials, disregarding the data for those nuclei known to be distorted does result in excellent agreement.