Abstract
The effective multiplication factor (keff) is the dominant eigenvalue for the linear particle transport operator. A proof for the existence of a simple dominant eigenvalue with a positive eigenfunction is established in the L1 setting in the presence of particle reflection at the domain boundary as characterized by a general integral albedo operator. By arguing that physics demands to work on an L1‐weighted space, a direct physical approach based on linearity and positivity allows us to circumvent some of the limitations encountered in the classical proofs.
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