Estimation of Nuclear Reaction Model Parameter Covariances and the Related Neutron Induced Cross Sections with Physical Constraints

In neutron induced reactions between 0 eV and 20 MeV, a general problem arises during the evaluation of cross sections. Most of the time, the evaluation work is done independently between the resolved resonance range and the continuum, giving rise to mismatches for the cross sections, larger uncertainties on boundary and no cross-correlations between high energy domain and resonance range. This paper will present several methodologies that may be used for avoiding such effects. A first idea based on the use of experiments overlapping two energy domains appeared in the near past. It will be reviewed and extended to the use of systematic uncertainties (normalization for example). In addition, we propose a methodology taking into account physical constraints on an overlapping energy domain where two nuclear reaction models are used (continuity of both cross sections or derivatives for example). The use of Lagrange multipliers (related to these constraints) in a classical generalized least square procedure will be presented and some academic examples will be detailed.