A complementary Doppler Broadening formalism and its impact on nuclear reactor simulation

The Boltzmann Transport equation is the governing formalism upon which simulations of nuclear reactors are performed, in particular when strong absorption or anisotropic scattering are significant. On the left (loss) hand side of the balance equation one finds the absorption and the scattering cross section Σa(E'), Σs(E') respectively. Those cross sections are energy and temperature dependent i.e. Doppler Broadened. The scattering cross section appears explicitly again on the right (production) hand side of the equation in its differential form ∫∫0∞Σ(E → E'; Ω → Ω')dE dΩ. However, this term is commonly evaluated at 0 K and it does not account for the existing resonances which are the underlying characteristic for Doppler Broadening. Evidently one gets an inherent inconsistency between the integral and differential scattering cross section within the transport solver codes. In this study this missing Doppler Broadened formalism for the differential scattering cross section is introduced in its stochastic and deterministic form. The impact on core criticality is shown to be up to 600 pcm and the change in the nuclides' inventory significant, in particular the 239PU content can be changed by several percents. (orig.)