New derivation of Blackshow–Murrays formula for the Doppler-broadened scattering kernel and calculation of the angular moments via Lagrange interpolation

Abstract A new independent derivation of Blackshow–Murray’s classical formula for the Doppler-broadening elastic scattering kernel is given, including an extension to anisotropy of scattering in the center of mass. Also, the puzzling behavior of the secondary angular and energy neutron distribution about the lower resonances of heavy isotopes is explained by introducing an asymptotic ordering, which includes on the same foot thermal agitation and resonance effects, and by a detailed analysis for the case of collinear scattering. Finally, we use Lagrange polynomial interpolations for a fast and accurate calculations of the angular moments of the kernel. Results for 238 U are presented, analyzed and compared to those in the existing literature, for both isotropic an anisotropic scattering in the center of mass.