Iterative and Direct Approaches to the Critical Dominant Eigenfunction in Three-Dimensional Neutron Transport

We present two methods, one iterative and the other direct, for the solution of the integral transport equation for monoenergetic neutrons in a three-dimensional finite system, made up of isotropically scattering and multiplying inhomogeneous materials. The methods are suggested by the physical characteristics of criticality, seen in the light of the mathematical concept of the dominance of the fundamental positive flux distribution. Additional results concern the lifecycle point of view for neutron chain reactions, the critical importance function, and the uniform convergence of the Neumann series in all subcritical cases.