On criticality problems in energy dependent neutron transport theory

AbstractIn this paper, we consider the criticality problem for energy dependent neutron transport in an isotropically scattering, homogeneous slab. Under a positivity assumption on the scattering kernel, we can find an expression relating the thickness of the slab to a parameter characterizing production by fission. This is accomplished by exploiting the Perron-Frobenius-Jentsch characterization of positive operators (i.e. those leaving invariant a normal, reproducing cone in a Banach space). We point out that those techniques work for classes of multigroup problems where the Case singular eigenfunction approach is not as feasible as in the one-group theory, which is also analyzed