Homogenization of a spectral equation in neutron transport

We study the homogenization of an eigenvalue problem for the neutron transport in a periodic heterogeneous domain. We prove that the neutronic flux can be factorized as a product of two terms, up to a remainder which converges strongly to zero with the period. The first term is the first eigenvector of the transport equation in the periodicity cell. The second term is the solution of an eigenvalue problem for a diffusion equation in the homogenized domain. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations.