Abstract

The use of operational calculus allows to obtain exact expressions for the resonance integral and the intermediate resonance parameters to be obtained. These expressions are obtained for the more general case of an heterogeneous system of one resonance absorber with N admixed moderators and M moderators. The trial functions for the fluxes needed in the calculus are obtained by means of a linear approximation for the slowing down operators. There, the intermediate resonance parameters are introduced with physical meaning. Three approximations are used for calculating the resonance integral, and they are applied to several resonances in homogeneous and heterogeneous systems. Then the three approximations are compared with Monte Carlo calculations. One of them is found to be in very good agreement with Monte Carlo results. Finally, the general formulation given here includes many of the I-R methods developed up to the present.

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