Universal curve of epithermal neutron resonance self-shielding factors in foils, wires and spheres

Dependence of thermal and epithermal neutron self-shielding on sample size and irradiation site

“…G th and G ep are the thermal and epithermal self-shielding factors for the given (n, g) reaction. These definitions of j th ,j ep , G th and G ep are consistent with those used in Monte-Carlo simulations [2][3][4] where j th and j ep are found by simulating a sample of infinite dilution. G th and G ep depend on sample geometry and they are equal to unity for sufficiently dilute samples.…”

“…Recently, Salgado et al [2,6] claimed that, for nuclides having one resonance or a few isolated resonances, G ep could be expressed by the same universal function, a sigmoid, with only one nuclide-dependent parameter. The same authors [3] extend their theory for cylindrical samples by introducing a sigmoid expression for G ep that fits the data generated by a Monte-Carlo calculation for a pure element sample irradiated in an isotropic neutron flux.…”

“…Regardless of the reactor type, for large samples and for samples with high concentrations of neutron absorbing elements, the equation used in k 0 neutron activation requires the knowledge of thermal and epithermal selfshielding factors. Recent studies [2][3][4] indicate that both self-shielding factors, G th and G ep , can be expressed by a sigmoid function with a parameter depending on the nuclide and the geometry and the composition of the sample. The sigmoid function was established for monoelement objects irradiated in an isotropic neutron field, conditions not applicable in the real NAA situation.…”

Application of the k0method in neutron activation analysis and in prompt gamma activation analysis

“…Methods were available for estimating and correcting thermal neutron self-shielding but none for epithermal neutron self-shielding except very difficult Monte-Carlo calculations. Then it was discovered that other researchers had an idea [62] for an analytical formula for epithermal self-shielding with only one nuclear constant to be determined for each nuclide. This was developed at Montreal by Chilian et al [33] and now the effective self-shielding factor, G eff , which is a combination of the thermal and epithermal self-shielding factors, G th and G ep , can be calculated for cylindrical samples easily and accurately with the following formula:…”

Estudo de técnicas estatísticas aplicadas à determinação de parâmetros no método <i>k₀</i> de análise por ativação neutrônica

“…Este efeito pode ser de considerável importância se a seção de choque da amostra exibir um relevante pico de ressonância para o campo de nêutrons considerado. Em uma situação típica, a atividade de um dado nuclídeo produzido pela reação (n, ) por meio da irradiação de uma amostra contendo uma quantidade de elemento é dada por: Uma função sigmóide universal foi desenvolvida para os cálculos de ℎ e [69,70] . Para nêutrons térmicos a expressão é dada por: A estimativa de como função da concentração do elemento a da geometria da amostra é uma tarefa complexa, em razão de cada nuclídeo possuir um padrão de ressonância diferente e às vezes complexo [71] .…”