Efficient Methods for the Treatment of Resonance Cross Sections

Abstract

Work has been done to develop improved methods for treating resonance cross sections in both the resolved and the unresolved energy regions. The methods are natural extensions of previous methods using the J* treatment. Efficient numerical algorithms have been developed to make the methods highly economical for the routine fast reactor calculations. For the resolved energy region, a new technique is proposed for evaluating the generalized form of the resonance integral which allows the use of the multilevel formalism. By taking advantage of the asymptotic behavior of the Doppler-broadened line-shape functions, the technique of rational transformation is introduced. Gauss-Jacobi quadrature is used to evaluate the integral with the transformed integrand. The integration can be carried out efficiently. For the unresolved energy region, an accurate and efficient method has been developed for estimating the effect due to in-sequence overlap. In contrast to the previously developed methods, the new method is capable of treating practically all energy regions of practical interest in fast reactor applications. The Dyson correlation function is used to account for the proper correlation of levels. The method has been made economical for routine calculations.