The resonance self-shielding calculation with regularized random ladders

In the last four years several papers have been published on the calculation of resonance self-shielding (Hwang, 1984; Munoz-Cobos et al., 1982; Sinitsa, 1983; Takano et al., 1980), and an international exercise organized under the auspices of the NEA is going on. Hereafter we shall restrict ourselves to the treatment of the unresolved energy range with the narrow resonance approximation. The straightforward method is to generate one or several resonance ladders, and to process them as resolved resonances. The main drawback of Monte Carlo methods, used to generate the ladders, is the difficulty of reducing the dispersion of data and results. Several methods have been suggested, that we examine, and we strongly recommend one of them. We consider in more detail how this method (a regularized sampling method) improves the accuracy. Analytical methods to compute the effective cross-section have recently appeared: they are basically exempt from dispersion, but are inevitably approximate. We check the accuracy of the most sophisticated one. There is a neutron energy range which is improperly considered as statistical: we examine what happens when it is treated as statistical, and how it is possible to improve the accuracy of calculations in this range. The present renewal of interest by reactor physicists in self-shielding results from the improvement of computer techniques, while it was realized that self-shielding factors may differ by 5–8%, even for important nuclei. They would be happy to reduce this error to 0.5%; we propose less as a long-term goal (10−3 for systematic errors), and then, within this paper, we will denote attention to differences greater than 10−4. To illustrate the results we have performed calculations in a simple case: nucleus 238U, at 300 K, between 4250 and 4750 eV, with ENDF-B 4 average parameters: D = 19.98 eV, \gGon = 0.0020979 eV and Γy = 0.0235 eV. More results are given in a previous report (Ribon et al., 1985).