Abstract

The method of Lebesgue moments for simulating the reversal of resonances, resonance self-shielding, and block effect in the neutron spectra of extended heterogeneous objects, such as nuclear reactors, radiation shielding, and installations for studying the properties of matter, is developed. The method uses a more accurate averaging procedure over neutron energy than the group averaging. The main components of the method are the refinement of the resonance structure of neutron cross sections by dividing the energy scale into a series of sets called carriers of resonances, Lebesgue averaging of cross sections and neutron flux within carriers, and the expansion of the neutron flux in a series in basis functions that depend on the magnitude of the neutron cross sections. The expansion coefficients (the so-called Lebesgue moments) can be calculated by any available method for solving the neutron transport equation.

中文翻译：

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用Lebesgue矩法求解中子输运方程。

摘要

开发了Lebesgue矩的方法，该方法用于模拟扩展的非均质物体（例如核反应堆，辐射屏蔽以及研究物质性质的装置）的中子光谱中的共振反转，共振自屏蔽和块效应。该方法在中子能量上使用比群平均更准确的平均过程。该方法的主要组成部分是通过将能级划分为一系列称为共振的载流子集，对截面和载流子中的中子通量进行勒贝格平均化以及中子通量的扩展来改进中子截面的共振结构一系列取决于中子截面大小的基础函数。