The Scattering of Fast Neutrons by Heavy Nuclei

Abstract

The experimental work of Dunning has shown that for fast neutrons the capture cross sections of heavy nuclei are small compared to their cross sections for elastic scattering. While it cannot be concluded from this that polarization effects (i.e., contributions to the elastic scattering from quasi-stationary states of the nucleus-neutron system) are negligible, it seemed worth while to investigate the results of a treatment neglecting polarization. We use the effective potential for a neutron in the field of a heavy nucleus developed by Van Vleck. The values of the constants of the inter-particle interactions are adjusted slightly from those found by Feenberg from binding energy calculations. The problem reduces to that of a neutron in the field of a potential well whose depth is a slowly varying function of the neutron velocity. The scattering problem is solved by the method of partial cross sections. Anomalous resonances due to the attractive potential are found in the higher partial cross sections. Although these resonances have anomalously high peaks it is shown that on account of their sharpness they contribute little to the cross section for a neutron beam having a broad velocity distribution. The cross section is found to vary markedly with both velocity and atomic number. Even for a broad velocity distribution corresponding to Dunning's experimental source oscillations remain in the cross section as a function of atomic number. However, the existing experimental points fit the curve within the experimental error. That the experimental results are in no case much larger than those given by the theory would perhaps indicate that contributions due to polarization effects are small. Possible experimental work to test the theory is mentioned.