The multipole method for the on-the-fly computation of the temperature dependency of nuclear cross-sections

In nuclear reactor physics, the knowledge of the cross-sections describing interactions of neutrons with the medium through which they diffuse is of paramount importance. These sections depend both on the energy of the neutron and the temperature of the medium. Concerning the energy dependency, cross-section profiles display, in general, numerous resolved resonances on the energy range of interest. The multipole representation is an additive and exact description of the resonant cross-sections at zero temperature. The temperature dependency is then computed by a linear operation using analytical tools such as the Faddeeva function. This thesis is devoted to the theoretical aspects of the multipole representation as well as two main applications. Concerning the theoretical study, we show that the number of required poles for the representation of sections under the Multi-Level Breit-Wigner and Reich-Moore formalisms can be reduced compared to previously established results. This requires, notably, a formal study of rational functions and solving polynomials of very high degree (superior to 50 and potentially reaching the thousands). Concerning the applications, the first one focuses on the implementation of the original theoretical elements found during the thesis. A reconstruction of sections at zero temperature and a comparison with reference results is proposed in order to prove the relevance and correctness of the newly computed multipole parameters. The results are extremely satisfying albeit limited by nature to resonant cross-sections. The second application consists in using the multipole representation for the Doppler broadening of cross-sections: a comparison to sections broadened with the usual method (so-called 'sigma-1') is presented. The results of this comparison are also very satisfying although some efforts are still necessary on the border of the energy domain of resolved resonances. In the context of Monte Carlo transport simulations, the linearity of the Doppler broadening and the additive nature of the multipole representation suggest that it is possible to compute cross-sections 'on-the-fly', at each neutron collision, which would allow strongly reducing the memory footprint compared to current approaches (tabulation in energy of the cross-section profiles at multiple temperatures). (author)