Calculation of actual cross sections and thermalization of neutrons

This report gathers and presents in a simple way results of studies performed at the CEA on issues of spectra in thermal reactors. It is in fact a synthesis of results eventually published in different documents. It first presents the notion of actual cross section as it was introduced by Westcott to characterize the dependence of neutron behaviour on speed distribution. It addresses the case of a homogeneous medium with a conventional model, with the heavy gas model, and with the hydrogen gas model. It generalizes the approach by the differential model. The next part addresses the case of a heterogeneous medium, and the case of presence of moderator nuclei within the fuel