High-Energy Neutron-Nuclei Total Cross Sections

Abstract

Total cross sections for collisions between high-energy neutrons and nuclei are calculated by means of the Glauber approximation. Both Woods-Saxon and Gaussian density distributions are assumed for the nuclei. The two distributions yield results which may differ from each other by as much as 15%. For light nuclei harmonic-oscillator wave functions are used. The calculations are compared with measurements for neutron energies above 1 GeV. A simple explanation is given to show why the dependence of the cross sections on the mass number $A$ is greater than ${A}^{\frac{2}{3}}$. Although the multiple scattering series for a mass-$A$ nucleus contains $A$ terms, it is shown that excellent accuracy is obtained by retaining only approximately $3{A}^{\frac{1}{3}}$ terms and a geometrical argument leading to this result is given. The ratios of the real to imaginary parts of the hadron-nuclei forward elastic scattering amplitudes are calculated and the decrease of their magnitudes with increasing mass number is explained. The neutron-nuclei data are consistent with little or no regeneration.