Mathematical models in Slowpoke reactor internal irradiation site

The main objective is to build representative mathematical models of neutron activation analysis in a Slowpoke internal irradiation site. Another significant objective is to correct various elements neutron activation analysis measured mass using these models. The neutron flux perturbation is responsible for the measured under-estimation of real masses. We supposed that neutron flux perturbation measurements taken during the Ecole Polytechnique de Montreal Slowpoke reactor first fuel loading were still valid after the second fuelling. .We also supposed that the thermal neutrons spatial and kinetic energies distributions as well as the absorption microscopic cross section dependence on the neutrons kinetic energies were important factors to satisfactorily represent neutron activation analysis results. In addition, we assumed that the neutron flux is isotropic in the laboratory system. We used experimental results from the Slowpoke reactor internal irradiation sites, in order to validate our mathematical models. Our models results are in close agreement with these experimental results..We established an accurate global mathematical correlation of the neutron flux perturbation in function of samples volumes and macroscopic neutron absorption cross sections. It is applicable to sample volumes ranging from 0,1 to 1,3 ml and macroscopic neutron absorption cross section up to 5 moles-b for seven (7) elements with atomic numbers (Z) ranging from 5 to 79. We first came up with a heuristic neutron transport mathematical semi-analytical model, in order to better understand neutrons behaviour in presence of one of several different nuclei samples volumes and mass. In order to well represent the neutron flux perturbation, we combined a neutron transport solution obtained from the spherical harmonics method of a finite cylinder and a mathematical expression combining two cylindrical harmonic functions..With the help of this model and the least squares method, we made extensive non linear accurate regression analyses of the experimental results..Also, we devised a numerical neutron transport model using the discrete ordinates method of S8 scheme. In both cases, we assumed a thermal neutrons Maxwell energy distribution since thermal neutrons are dominant in internal sites. In addition, both of our models used energy dependant microscopic neutron absorption cross sections. .In order to implement and use these mathematical models, we chose to use computer algebra software instead of the more usual ones. The Slowpoke reactor internal irradiation site neutron transport semi-analytical model results are within 1% of the flux perturbation experimental results which is well within the experimental results error at about 2%. The discrete ordinates numerical method results obtained from a 2-D finite cylinder shows an average error of about 3% and a variance of about 2% as compared to the experimental results. The semi-analytical and numerical models clearly confirm that the results for many different elements are located on a unique flux perturbation curve as a function of the macroscopic absorption cross section for a given sample volume. Both models of a Slowpoke internal irradiation site are in close agreement with the experimental flux perturbation results. We devised a rapid (ms) accurate (ng) measured concentration correction computing algorithm for an internal irradiation site that can be easily implemented in the existing neutron activation laboratory EPAA software. This corrective method accurately compensates the flux perturbation effect. This process allows more accurate concentration measurements for many elements on a wider concentration range. (author)