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

Abstract

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.

Stimulated perturbation on the neutron flux distribution in the mutually-dependent source-to-absorber geometry

“…1. These absorbers are made of either strong absorber (indium, gold, or mercury) or weak absorbers (iron or zinc), and selected to have different thermal neutrons cross sections and resonance integrals [19][20][21]. The unit is the probability of emission divided by the unit lethargy of the preceding energy domain.…”

“…Indium has two isotopes 115 In (IA = 0.95719) and 113 In (IA = 0.04281) [22]. For 115 In, the thermal neutron absorption cross section is σ 0 =202.22 b while the resonance integral in pure 1/E-neutron spectrum is I 0 =3211 b [20,21,23,24]. However, the thermal neutron cross section and resonance integral for the specific reaction 115 In(n,γ) 116m In are 162.6 b and 2585 b [6], respectively.…”

“…113 In, however, has small value of isotopic abundance and much smaller thermal neutron cross section and resonance integral, i.e. σ 0 =12.13 b and [20,21,23,24], so 113 In has a limited contribution to the overall macroscopic cross section of the element. In our MCNP simulation, positioning indium absorber in the center of mass of the pile causes a reduction in the total thermal flux within the void no.…”

“…Gold is a mono-isotope element having only 197 Au whose thermal neutron absorption cross section is σ 0 =98.65 b while the resonance integral in pure 1/Eneutron spectrum is I 0 =1567 b [20,21,23,24]. 197 Au, however, has an intense neutron resonance at 4.89 eV with capture width of Γ γ =0.124 eV [20,23]. Such large resonance had an implication on the effect of gold on neutron field perturbation as shown in Fig.…”

“…The next strong absorber is mercury. Mercury has 7 stable isotopes, including 198 [ [20][21][22][23][24]. The strongest absorber among them is 199 Hg.…”