The Ribon Extended Self-Shielding Model

Improvement of the lattice code component related to resonance self-shielding calculations is described. The proposed selfshielding model is based on a subgroup flux equation with probability tables, as implemented in the CALENDF approach of P. Ribon. A new type of correlated two-dimensional probability table is introduced for the representation of the slowing-down effect in the resolved energy domain. The resulting formalism makes possible a better representation of distributed self-shielding effects. A new numerical scheme is also proposed to represent the mutual shielding effect of overlapping resonances between different isotopes in the context of the Ribon subgroup equations. The interference effects between two resonant isotopes are represented by a correlated weight matrix also computed using a CALENDF approach. The model was designed with the primary goal of allowing the straightforward replacement of legacy self-shielding components in typical lattice codes to gain improved accuracy without any noticeable increase in CPU resources. Finally, a validation is presented where the absorption rates are compared with exact values obtained using a fine-group elastic slowing-down calculation in the resolved energy domain. Other results, relative to Rowlandʹs pin-cell benchmarks, are also presented. The need to represent mutual shielding effects, at least for mixed-oxide fuel is demonstrated.