Averaging of the neutron transport equation over energy by the Lebesgue moment method
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 (the Sn method, the spherical harmonics method, and the Monte Carlo method).