Approximate processing of the level-level interference in an R-matrix formalism

This work is devoted to an evaluation of the integral coefficients of neutron resonances directly from resonance parameters, which enables the evaluation of individually distinct single-resonance integrals. Individually distinct single-resonance integrals are useful when investigating the statistical nature of resonance distribution, the role of the neutron flux shape parameter, applications in nuclear reaction physics, isotope synthesis in reactors and astrophysical entities, activation analysis, and the science of nuclear materials. The present R-matrix treatment comprises exact expressions for the Breit-Wigner resonance representation and approximate expressions for the Reich-Moore representation; the latter is used to avoid the complicated techniques used for matrix inversion. The analytical formulae are used to evaluate the necessary integral neutron coefficients directly from spectroscopic nuclear data. Using the analytical formulae, the resonance integrals and the effective resonance energy can be taken into consideration for any specific values of epi-thermal shape parameter. In addition, the atomic displacement densities can be computed with variable threshold energies for atomic displacements. A Fortran code, NEURESINT, designed to perform these calculations is given in the manuscript's supplementary material available online at stacks. iop. org/PS/94/065301/mmedia. The code is used to compare integral coefficients among different versions of evaluated nuclear data files. The present approximation gives thoroughly consistent results with the reported values of integral parameters. Our results showed that care must be taken when applying the methods and code mentioned in the present work to some isotopes, especially actinides having a resonance level close to the epi-cadmium cutoff energy at 0.55 eV, in which much smaller cutoff energy value, as low as 0.1 eV, needs to be used.