On the neutron spectrum and multiplication factor in the infinite homogeneous reactor

The analysis of the infinite homogeneous reactor can be useful to have a quick understanding of nuclear reactor phenomena. Thanks to the fact that the neutron emission spectrum from fission is modeled in order to depend neither on the energy of the incident neutron nor on the fissioning nuclide, the critical neutron balance equation can be transformed from an eigenvalue problem to a simple inhomogeneous system. Similar considerations can be addressed to the adjoint problem and to the generalized importance, which can be computed with direct expressions. After having derived the equations relative to the above quantities, we apply them to the investigation of some features of the neutron spectrum in UO2 and MOX fuel. We deduce some relationships between the properties of the medium and the neutron spectrum, such as the independence of the neutron spectrum from the fission cross section and the neutron multiplicity. We show also in which extent these conclusions can be applied to real reactors.