Monte Carlo calculation of resonance self-shielding factors for epithermal neutron spectra varying as E-(1+α)

In nuclear reactor physics it is usual to consider the neutron field divided into three energy groups: thermal neutrons (E ≤ 0.5 eV; Maxwellian spectrum), epithermal neutrons (0.5 eV < E < 0.1 MeV; spectrum varying as E-(1+α)), and fast neutrons (0.1 MeV < E < 10 MeV; fission spectrum). In order to characterise experimentally the neutron spectra, activation detectors are generally used (foils or wires). The materials must have appropriated cross sections: cross section varying as 1/v for thermal neutrons; well defined resonance for E = E(res) in the energy range of epithermal neutrons; and threshold cross section (σ ≠ 0 for E ≥ E(threshold) for fast neutrons. It is known that the activation detectors induce a neutron flux perturbation due to self-shielding effect, which can be larger or smaller depending on the detector characteristics. The self-shielding factor, G, depends mainly on the material used, the reaction cross-section and the thickness t (for foils) or radius R (for wires). The thermal neutron self-shielding factor, G(th), can be determined through universal curves, as a function of the dimensionless parameter z = Σt or z = ΣR, where Σ represents the total macroscopic cross section. In general, the fast neutron self-shielding factor, G(fast), can be taken as 1, since the fast neutron cross sections are relatively small. In this work, the resonance self-shielding factor, G(res), is calculated by means of the Monte Carlo technique. The considered variables are (a) the material type, and the detector geometry and dimensions; (b) the parameter α which characterises the deviation of the epithermal neutron spectrum to the 1/E law (α = 0 for an infinite, non-absorbing medium); and (c) the incidence of the neutrons (isotropic field or collimated beam). The results are compared with published experimental and calculated values. Besides the utilisation of G(res) in neutron spectrometry, the knowledge of this parameter is also useful for the determination of the epithermal neutron flux, Φ(epi), and for the evaluation of the contribution of epithermal neutrons to the electrical current of self-powered neutron detectors and to the activation of samples, which can be significant if the resonance integral of the material is high compared to the activation cross section for thermal neutrons. (author)