Abstract
A consistent description of the neutron cross sections from thermal energy up to the MeV region is challenging. One of the first steps consists in optimizing the optical model parameters using average resonance parameters, such as the neutron strength functions. They can be derived from a statistical analysis of the resolved resonance parameters, or calculated with the generalized form of the SPRT method by using scattering matrix elements provided by optical model calculations. One of the difficulties is to establish the contributions of the direct and compound nucleus reactions. This problem was solved by using a slightly modified average R-Matrix formula with an equivalent hard sphere radius deduced from the phase shift originating from the potential. The performances of the proposed formalism are illustrated with results obtained for the 238 U+n nuclear systems.
Highlights
We can observe that there is a continuous transition from the extreme situation of well-isolated resonances to complete overlap
The SPRT method is used to study the consistency between the average R-Matrix parameters adjusted on experimental data and those given by optical model calculations
The main conclusion of this work is that the SPRT method yields s-wave and d-wave neutron strength functions of similar magnitude and nearly independent of the neutron energy: S0 S2 cst, if and only if the optical model and its equivalent squarewell provide the same phase shifts at the common channel radii ac
Summary
We can observe that there is a continuous transition from the extreme situation of well-isolated resonances to complete overlap. This transition was first described by Feshbach et al [1], explaining how the R-Matrix and optical models may coexist between the “resonance region” and the “continuum region”. The main ingredients of the theory of average cross section are given in this document. Equations are slightly modified to account for direct reactions by introducing complex background terms in the ReichMoore approximation of the R-Matrix theory [2]. Consequences on the neutron strength functions calculated in the hard sphere approximation are discussed with results provided by the OPTMAN code
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