A Schematic Theory of Nuclear Cross Sections

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Abstract
In this paper a description of the energy dependence of nuclear cross sections, especially for neutrons, is given in terms of simple assumptions on the properties of the nuclei. The results are supposed to represent average values over individual fluctuations and resonances. The total cross section, the reaction cross section, and the transport cross section are calculated as functions of the neutron energy. Only two nuclear parameters occur in the expressions; the nuclear radius and the average kinetic energy of a nucleon inside the nucleus. Comparison of the theory with neutron experiments is made. New values of nuclear radii are computed from total cross sections at 14 and 25 Mev. Predictions of the inelastic cross sections at 14 Mev are in good agreement with the measurements. Experiments involving total and transport cross sections between 0.1 and 1.5 Mev are compared with theory and reasonably good agreement is found with most of these. However, for the elements, I, In, Sb, agreement in the context of the theory may be obtained only if the strength of resonance levels for these elements is assumed to be unusually low.