The moment method of Lebesgue aggregation and spectrum recovery in particle transport problems

The method of spectral moments that simplifies the calculation of nonmonotonic multiresonance spectra of neutrons or photons in the problems of nuclear technologies, radiating plasma and atmospheric radiation is developed. The particle distribution function is expanded in basis functions that depend on the particle energy and the resonance structure of the cross sections, and ensure fast convergence of the expansion. Efficient way of finding the series expansion coefficients (spectral moments) based on the solution of the transport equation for the Lebesgue distribution of particles on the system of Lebesgue sets is described. Fast convergence of the expansion is shown in test problems.