A multi-group analytical model for the kinetic parameters

In the framework of the Verification&Validation activities conducted by newcleo for its Lead-cooled Fast Reactor design tools, this work presents an analytical derivation of reactor kinetic parameters within the multi-group diffusion theory for homogeneous systems. Explicit expressions for the forward and adjoint fluxes are obtained, enabling closed-form evaluations of βeff and Λeff. The proposed model provides physical insight into the group-wise contribution of kinetic parameters and serves as a reference for verifying numerical codes. Despite its simplifying assumptions, it offers valuable benchmarks for liquid-metal fast reactors and paves the way for future extensions including finer group structures, analytical sensitivities, and up-scattering effects.