Open issues on scattering kernels of compound nuclear reactors

Scattering kernel models, define the energy change and angular distribution of a scattered neutron. In the keV and fast energy ranges these are often determined by phenomenological concepts or using fits to measurements due to lack of microscopic details and/or complicated mathematical issues with some models. Some scattering kernels neglect the temperature dependency or the resonant structure of the nuclide. Moreover, most of the double differential solutions do not sum up mathematically to the integral scattering cross section itself and are in the best case artificially adapted. This study deals with the scattering kernel of compound nuclei in energy ranges mainly up to 50 keV, for structured resonance cases. It compares the two advanced approaches as far as the physics is concerned, one of which is based on classical kinematics with a quantum correction in form of the energy dependent resonances developed by Rothenstein-Dagan (RD), and the other model by Blatt-Biedenharn (BB) resembles. Both models are based on theoretical microscopic assumptions yet differ by their physics approach. The analysis in this study leads to two new main observations. On one side the importance of inclusion of the azimuth angle, and further for a quantum mechanics approach a unique mutual spin number must be defined for the total cross-section as well as the angular distribution measurements.